# Quiz 12: Annuities: Special Situations

Business

Q 1Q 1

Moses' goal, when he retires from work in seven years, is to have $400,000 in his Retirement Fund. Assuming he achieves his goal and the fund earns 7% compounded semi-annually after he retires, what is the amount that Moses will be able to take out of his Retirement Fund at the end of every six months for 25 years after he retires?
A) $17,053
B) $24,270
C) $28,984
D) $3,053
E) $6,324

Free

Multiple Choice

A

Q 2Q 2

What is the economic value today of 24 monthly payments of $500 with the first payment occurring 10 months from today? Assume that money can earn 12% compounded monthly.
A) $9,711.84
B) $8,973.34
C) $10,621.69
D) $9,615.68
E) $13,486.73

Free

Multiple Choice

A

Q 3Q 3

Fred purchased a farm with a down payment of $8,500 and 48 semi-annual payments of $3,000. The first of these payments is to be made two years after the date of purchase. What was the purchase price of the farm if the interest rate charged on the balance is 14% compounded semi-annually?
A) $41,191.42
B) $31,424.74
C) $42,124.47
D) $39,924.74
E) $49,691.42

Free

Multiple Choice

C

Q 4Q 4

Calculate the present value of a deferred annuity of 20 annual payments of $25,000 each The interest rate is 8.5% compounded annually and the first payment will be made in six years.
A) $306,472
B) $211,760
C) $157,339
D) $145,013
E) $104,289

Free

Multiple Choice

Q 5Q 5

Heather is planning to retire in 10 years. She will then need an income of $1,500 at the end of every month for the subsequent 25 years. She is going to make one investment today to provide all of the money she will eventually collect. Her investments will earn 12% compounded monthly. How much should she invest today?
A) $43,152.46
B) $67,449.00
C) $92,461.46
D) $139,437.52
E) $167,687.74

Free

Multiple Choice

Q 6Q 6

Evergreen Landscaping is applying for a loan. Your help is needed to determine how much they can borrow. They will not be able to make any payments for the first 18 months. After that, they will make payments of $750 per month for five years. There is no interest-free grace period. The first $750 payment will be made 18 months after the loan is received. If the interest rate is 10.5% compounded monthly, how much can they expect to borrow?
A) $29,829
B) $34,894
C) $36,515
D) $30,090
E) $24,008

Free

Multiple Choice

Q 7Q 7

Hard Rock Paving Company is applying for a loan. It is your job to determine how much they will be able to borrow. They will not be making any payments for the first 15 months. After that, they will make payments of $1,000 per month for four years. There is no interest-free grace period. The first $1,000 payment will be made 15 months after the loan is received. If the interest rate is 13.2% compounded monthly, how much can they expect to borrow?
A) $37,138
B) $31,864
C) $31,517
D) $33,915
E) $40,736

Free

Multiple Choice

Q 8Q 8

Harold is planning to retire in 21 years. After that he will need an income of $4,500 at the end of every month for the subsequent 25 years. He is going to make one investment today to provide all of the money he will eventually collect. His investments will earn 9% compounded monthly. How much should he invest today?
A) $103,817
B) $104,397
C) $81,582
D) $82,194
E) $205,390

Free

Multiple Choice

Q 9Q 9

Calculate the present value of a deferred annuity of 20 annual payments of $100,000 each The interest rate is 13.5% compounded annually and the first payment will be made 11 years from now.
A) $169,340
B) $593,451
C) $218,148
D) $681,890
E) $192,201

Free

Multiple Choice

Q 10Q 10

Anita is planning to go back to school in 2 years. Once at school, she wishes to be able to withdraw $900 at the end of each month for 2 years. If interest is 4.5% compounded monthly, determine the amount that should be deposited now to fulfil her goal.
A) $18,848.06
B) $19,675.25
C) $20,437.43
D) $20,884.13
E) $21,973.28

Free

Multiple Choice

Q 11Q 11

Gregory deposits a $30,000 for a period of time at a 3.5% rate of interest compounded semi-annually. The accumulated amount provides Gregory the benefit of withdrawing $1,165 at the end of each month for three years. Determine how long the initial deposit accumulated interest.
A) 3 years
B) 4 years
C) 5 years
D) 6 years
E) 7 years

Free

Multiple Choice

Q 12Q 12

Andy deposits $40,000 into an account earning 6.6% compounded annually for 5 years. After this time, Andy wishes to withdraw $2,814.41 at the end of each quarter and have $10,000 remaining. Determine the number of withdrawals Andy can make.
A) 20 withdrawals
B) 24 withdrawals
C) 28 withdrawals
D) 32 withdrawals
E) 36 withdrawals

Free

Multiple Choice

Q 13Q 13

A purchase agreement for a $22,000 truck requires 60 equal payments every six months. If the first payment is due one year after the date of purchase and interest is charged at 18% compounded monthly, what is the size of each payment?
A) $2,065.46
B) $1,888.95
C) $1,991.31
D) $2,469.50
E) $2,258.47

Free

Multiple Choice

Q 14Q 14

An individual wants to receive end-of-month payments of $1,200 for 20 years after she retires 15 years from now. What lump amount must she invest today to provide the retirement income? Assume the investment earns 7% compounded monthly for the entire 35 years.
A) $49,864.93
B) $54,645.42
C) $54,328.50
D) $187,835.65
E) $155,681.89

Free

Multiple Choice

Q 15Q 15

Fred intends to retire in 10 years. To supplement his pension, he would like to receive $500 every six months for 20 years. If he is to receive the first payment six months after the date of his retirement, what lump amount must he invest today to achieve his goal? Assume that the investment will earn 12% compounded semi-annually.
A) $2,486.50
B) $4,871.78
C) $5,164.09
D) $2,345.75
E) $2,212.97

Free

Multiple Choice

Q 16Q 16

Harry deposits $10,000 into an investment account that earns 7% compounded monthly. How many monthly withdrawals of $310 will he be able to make if his first withdrawal is exactly five years after his deposit?
A) 36
B) 40
C) 54
D) 41
E) 53

Free

Multiple Choice

Q 17Q 17

Mrs. O'Halloran gave $130,000 to the University of Northern British Columbia for a perpetual scholarship fund. What amount can be awarded on each anniversary if the scholarship fund earns 7% compounded annually?
A) $13,000
B) $1,300
C) $1,857
D) $9,100
E) $91,000

Free

Multiple Choice

Q 18Q 18

The Pithybottoms want to make a donation to set up a scholarship trust fund at Hinose College. The fund is to support payments of $5,000 at the end of every three months in perpetuity. If the fund earns 7.5% compounded quarterly, how much must they donate?
A) $666,667
B) $375,000
C) $266,667
D) $66,667
E) $200,000

Free

Multiple Choice

Q 19Q 19

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?
A) $1,575
B) $1,890
C) $2,100
D) $15,750
E) $18,900

Free

Multiple Choice

Q 20Q 20

What amount can be paid at the end of every month, in perpetuity, from an endowment of $75,000 earning 8% compounded monthly?
A) $800
B) $750
C) $500
D) $400
E) $250

Free

Multiple Choice

Q 21Q 21

If an endowment fund of $2,327,000 is to be used to pay out grants of $175,000 at the end of every year in perpetuity what effective rate of interest must the funds earn?
A) 11.61%
B) 10.06%
C) 8.93%
D) 7.52%
E) 5.44%

Free

Multiple Choice

Q 22Q 22

What amount, invested today at 6% compounded monthly, will support perpetual monthly payments of $500? The first payment will be made one month from now.
A) $500,000
B) $400,000
C) $300,000
D) $200,000
E) $100,000

Free

Multiple Choice

Q 23Q 23

What amount, invested today at 5% compounded quarterly, will support perpetual monthly payments of $800? The first payment will be made one month from now.
A) $116,327
B) $192,798
C) $160,000
D) $63,997
E) $322,700

Free

Multiple Choice

Q 24Q 24

Simon Fraser recently received a $20 million donation to be used for scholarship purposes. If interest can be earned at 4.2% compounded monthly, determine the semi-annual amount of scholarships that students can apply for.
A) $423,692.20
B) $428,550.12
C) $431,084.45
D) $441,289.72
E) $444,821.94

Free

Multiple Choice

Q 25Q 25

A local college provides annual scholarships totalling $5,000 to business students. If interest is at 3.1% compounded quarterly, determine the original amount that was deposited.
A) $153,282.84
B) $156,857.13
C) $159,427.39
D) $160,834.67
E) $161,349.04

Free

Multiple Choice

Q 26Q 26

The Willie P. Stanton Trust Fund is to pay, $5,000 at the end of every year to the student-athlete voted most deserving based on his or her dedication to the ideals of good citizenship. The Trust Fund earns 7.4% compounded semi-annually. What is the present value of this perpetuity?
A) $66,340
B) $129,526
C) $72,341
D) $135,135
E) $67,568

Free

Multiple Choice

Q 27Q 27

What is the present value of a trust fund that earns 9% compounded monthly and pays out $950 every month into perpetuity? The next payment will be made today.
A) $126,667
B) $105,556
C) $141,667
D) $127,617
E) $95,950

Free

Multiple Choice

Q 28Q 28

The National Museum has received a donation of $2,000,000 which is to be used to purchase new exhibits at the end of every three months. If the money earns 12% compounded annually, how much could be paid out every three months in perpetuity?
A) $60,000
B) $57,475
C) $24,000
D) $114,704
E) $72,895

Free

Multiple Choice

Q 29Q 29

A $450,000 trust fund earns 8% compounded semi-annually. It is to make perpetual payments at the end of every month. What will be the size of the monthly payments?
A) $3,000
B) $1,800
C) $1,955
D) $2,453
E) $2,951

Free

Multiple Choice

Q 30Q 30

What amount can be paid at the end of every six months, in perpetuity, from an endowment of $475,000 earning 7% compounded annually?
A) $16,625
B) $16,344
C) $15,682
D) $14,971
E) $11,579

Free

Multiple Choice

Q 31Q 31

Calculate the present value of a perpetuity that will pay out $7,500 every six months. The first payment will be made four years from now. The interest rate earned is 8.6% compounded semi-annually.
A) $174,419
B) $129,898
C) $124,543
D) $119,563
E) $104,826

Free

Multiple Choice

Q 32Q 32

If a donation of $100,000 is expected to pay out scholarships of $10,000 every year and the funds earn 7.5% compounded annually, how long will it be before the first annual payment can be made?
A) 3 years
B) 5 years
C) 7 years
D) 9 years
E) 11 years

Free

Multiple Choice

Q 33Q 33

You wish to donate $10,000 to a local charity in order for it to provide annual benefits of $750 per year in perpetuity. If interest is compounded monthly, determine the interest rate needed to fulfil this goal.
A) 8.25%
B) 8.00%
C) 7.75%
D) 7.50%
E) 7.25%

Free

Multiple Choice

Q 34Q 34

A wealthy donor made a $50,000 contribution to a local charity. The charity invested this amount for three years at an interest rate of 2.4% compounded annually. At the end of this time, the charity wished to provide monthly benefits in perpetuity to those in need. Determine the amount that the charity can provide on a monthly basis.
A) $125.12
B) $114.74
C) $108.66
D) $106.21
E) $103.90

Free

Multiple Choice

Q 35Q 35

An endowment fund of $5,000,000 is to pay out grants for medical research. The grants are to be paid once per month and the first one is to be paid today. The fund will earn interest at 11% compounded semi-annually. What is the size of the monthly grants?
A) $45,833
B) $27,500
C) $39,782
D) $44,419
E) $44,817

Free

Multiple Choice

Q 36Q 36

A donation of $250,000 is made today to the local library for the purchase of new books. What amount can be withdrawn every month in perpetuity if the money is earning 9% compounded monthly and the first payment is to be made immediately?
A) $2,250.00
B) $1,875.00
C) $1,861.04
D) $1575.00
E) $1562.77

Free

Multiple Choice

Q 37Q 37

What is the present value of a trust fund that earns 8.8% compounded annually and pays out $3,500 every three months? The next payment is due to be made today.
A) $164,249
B) $745,820
C) $167,749
D) $529,722
E) $526,222

Free

Multiple Choice

Q 38Q 38

A trust fund of $55,000 is invested at 8.4% compounded monthly. It is to be left to accumulate interest for five years after which it is to support, in perpetuity, equal payments to be made at the end of every month. What will be the size of the payments?
A) $385
B) $585
C) $741
D) $916
E) $1,126

Free

Multiple Choice

Q 39Q 39

A wealthy benefactor has donated $1,000,000 to establish a perpetuity that is to pay a constant payment once per month. The money will earn 10% compounded annually. The first monthly perpetual payment will be made 28 months from now. Determine the size of the payments.
A) $9,960
B) $10,000
C) $9,881
D) $8,603
E) $10,047

Free

Multiple Choice

Q 40Q 40

Calculate the present value of a perpetuity that will pay out $1,500 every month and the first payment is to be made 10 years from now. The interest rate earned is 9% compounded annually.
A) $81,587
B) $82,199
C) $92,761
D) $88,546
E) $87,913

Free

Multiple Choice

Q 41Q 41

An 18-year-old college student plans to save a "Buck-A-Day" in a glass jar and after one year, set up a Retirement Savings Plan with $365. One year later he will make his second contribution to the RSP but it will be 10% larger than the first one. He will continue to increase his annual contributions by 10%. He anticipates that his investments can earn an annual return of 12.5% compounded annually. How much money is he expecting to have in the RSP after 40 years?
A) $773,510
B) $1,529,444
C) $1,411,823
D) $962,720
E) $284,291

Free

Multiple Choice

Q 42Q 42

How much money would accumulate over 35 years if the investor makes an investment of $3,500 at the end of the first year and always increases the size of the annual investment by 5% over the previous year. The investments are expected to earn 11% compounded annually.
A) $1,195,563
B) $1,928,432
C) $1,010,619
D) $1,624,915
E) $2,311,587

Free

Multiple Choice

Q 43Q 43

An investment of $50 is to be made at the end of this month and that amount is increased by 1% every month for 40 years. The investments are expected to earn 13.2% compounded monthly. What should be the total value of these investments in 40 years?
A) $3,607,093
B) $862,680
C) $1,847,397
D) $997,481
E) $2,646,194

Free

Multiple Choice

Q 44Q 44

Mary needs a pension that will pay her $12,000 one year from now and annual payments for 24 more years that are each 5% larger than the previous year. If the funds in her Retirement Fund earn 7.5% compounded annually, how much money must she have there now?
A) $188,490
B) $266,540
C) $532,842
D) $213,460
E) $487,671

Free

Multiple Choice

Q 45Q 45

How much will it cost to purchase a 20-year indexed annuity in which the end of quarter payments start at $6,000 and grow by 0.5% every quarter? Assume that the money used to purchase the annuity earns 8% compounded quarterly.
A) $277,727
B) $480,000
C) $316,842
D) $516,667
E) $326,744

Free

Multiple Choice

Q 46Q 46

We will make annual RRSP contributions at the end of every year for 35 years and each contribution is going to be 8% larger than the previous one. Our goal is to have $2,000,000 in 35 years. The RRSP will earn 13% compounded annually. How large will the first contribution be?
A) $1,048
B) $1,483
C) $1,746
D) $2,295
E) $3,742

Free

Multiple Choice

Q 47Q 47

We are aiming to have $5,000,000 in 45 years and we plan to get there by making monthly investments that are 1% larger than the previous month's investment. Our funds will earn 14.4% compounded monthly. How much should be invested at the end of the first month?
A) $24.29
B) $68.82
C) $103.74
D) $425.16
E) $801.93

Free

Multiple Choice

Q 48Q 48

Barklay has $782,490 in his Retirement Saving Plan and he wants to start receiving income at the end of every three months for the next 22 years. The funds earn 7% compounded quarterly and he wants each payment that he receives to be 1.5% larger than the previous one. How much will the first payment be three months from now?
A) $2,675
B) $6,429
C) $10,050
D) $15,829
E) $17,767

Free

Multiple Choice

Q 49Q 49

A loan of $126,500,000 is to be repaid by annual payments for 25 years. The payments will form a constant growth annuity with each payment being 20% larger than the previous one. The interest rate charged on the loan is 11% compounded annually. What is the size of the first payment?
A) $1,890,589
B) $2,729,835
C) $5,060,000
D) $9,756,417
E) $15,020,641

Free

Multiple Choice

Q 50Q 50

Calculate the present value of a 25-year annuity making semi-annual payments that grow at a rate of 4% compounded annually. The first payment is $25,000 and the funds earn 8% compounded semi-annually.
A) $606,574.51
B) $676,574.51
C) $706,574.51
D) $776,574.51
E) $876,574.51

Free

Multiple Choice

Q 51Q 51

Nino plans to initially contribute $10,000 and increase his yearly contributions by 2% each year for 15 years. If the rate of interest is 4% compounded annually, determine how much the investment will be worth in 15 years.
A) $227,537.58
B) $229,537.58
C) $231,537.58
D) $233,537.58
E) $235,537.58

Free

Multiple Choice

Q 52Q 52

Christian plans to initially contribute $3,000 and increase his yearly contributions by 5% each year for 20 years. If the rate of interest is 7% compounded annually, determine the amount of his payment in year 12.
A) $5,387.56
B) $5,687.56
C) $5,987.56
D) $6,287.56
E) $6,587.56

Free

Multiple Choice

Q 53Q 53

Edward wishes to have $450,000 in his retirement plans in 25 years. He plans to make annual contributions that will increase by 1% each year. If interest is earned at 5% compounded annually, determine the value of the initial payment in year 1.
A) $6,555.45
B) $7,005.45
C) $7,555.45
D) $8.005.45
E) $8,555.45

Free

Multiple Choice

Q 54Q 54

Baba Lou plans to retire in 20 years. At that point, he plans to collect payments at the end of every six months that are 2% larger than the previous payment, and this is to continue for 30 years. The first payment will be $16,500. His retirement plan is expected to earn 7% compounded semi-annually after he retires and 10% compounded annually before he retires. What single investment should he make now to fund the whole retirement plan?
A) $68,590
B) $95,411
C) $241,917
D) $316,443
E) $641,877

Free

Multiple Choice

Q 55Q 55

What amount of money invested now will provide monthly payments of $200 for five years, if the ordinary annuity is deferred for 3½ years and the money earns 3.75% compounded monthly?

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Short Answer

Q 56Q 56

Mr. Haddit plans to retire eight years from today. He projects that he will need $30,000 per year in his retirement which he assumes will be for 15 years. The first payment will be nine years from today. To fund his retirement, Mr. Haddit will invest a lump amount today and later use it to sustain the 15 withdrawals. If his investment earns 6% compounded annually, how much must he invest today?

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Short Answer

Q 57Q 57

Marion's grandfather will establish a trust that will pay her $1,500 every three months for 11 years. The first payment will be made six years from now, when she turns 19. If money is worth 6.5% compounded quarterly, what is today's economic value of the bequest?

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Short Answer

Q 58Q 58

Using an inheritance he recently received, Sam wants to purchase a deferred annuity that will pay $5,000 every three months between age 60 (when he plans to retire) and age 65 (when his permanent pension will begin). The first payment will be received three months after he reaches 60, and the last payment will be received on his 65

^{th}birthday. If Sam's current age is 50 years and 6 months and the invested funds will earn 4.4% compounded quarterly, what amount must he invest in the deferred annuity?Free

Short Answer

Q 59Q 59

A conditional sale contract requires the debtor to make six quarterly payments of $569, with the first payment due in six months. What amount will a finance company pay to purchase the contract on the date of sale if the finance company requires a rate of return of 16% compounded quarterly?

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Short Answer

Q 60Q 60

What amount of money invested now will provide payments of $500 at the end of every month for five years following a four-year period of deferral? The money will earn 5.4% compounded monthly.

Free

Short Answer

Q 61Q 61

How long is the period deferral if the first quarterly payment of a deferred annuity will be paid 3½ years from today?

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Essay

Q 62Q 62

Negotiations between Delco Manufacturing and the union representing its employees are at an impasse. The union is seeking a 4.5% wage increase. Delco's offer is 2%. The employees have passed a vote authorizing job action. Suppose the union succeeds in winning the 4.5% increase after a two-month strike. For an employee 10 years from retirement, will there be any economic gain? Compare the current economic values of (1) 10 years' end-of-month wages at the employer's offer (102% of last year's wages) vs. (2) wages including a 4.5% increase to the same horizon but after a two-month strike. Assume money is worth 6% compounded monthly.

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Essay

Q 63Q 63

A $35,000 loan bearing interest at 10% compounded quarterly was repaid, after a period of deferral, by quarterly payments of $1573.83 over 12 years. What was the time interval between the date of the loan and the first payment?

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Short Answer

Q 64Q 64

A $20,000 investment will be allowed to grow at 4.5% compounded semi-annually until it can support semi-annual withdrawals of $1,000 for 20 years. Rounded to the nearest month, how long before the first withdrawal must the investment be allowed to grow?

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Essay

Q 65Q 65

Mrs. Corriveau has just retired at age 58 with $299,317 in her RRSP. She plans to live off other savings for a few years and allow her RRSP to continue to grow on a tax-deferred basis until there is a sufficient amount to purchase a 25-year annuity paying $2,000 at the end of each month. If her RRSP and the annuity each earn 3.75% compounded monthly, how much longer must she let her RRSP grow (before she buys the annuity)?

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Short Answer

Q 66Q 66

What is the current economic value of an inheritance that will pay $2,000 to the beneficiary at the beginning of every three months for 20 years, starting when the beneficiary reaches 20 years of age, 4½ years from now? Assume that money is worth 6% compounded monthly. (Round to the nearest dollar.)

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Short Answer

Q 67Q 67

During a one-week promotion, Al's Appliance Warehouse is planning to offer terms of "nothing down and nothing to pay for four months" on major appliances priced above $500. Four months after the date of sale, the first of eight equal monthly payments is due. If the customer is to pay interest at the rate of 12% compounded monthly on the outstanding balance from the date of sale, what will be the monthly payments on an automatic dishwasher priced at $995?

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Short Answer

Q 68Q 68

Mr. Donatelli moved from Toronto to Winnipeg to take a job promotion. After selling their Toronto home and buying a home in Winnipeg, the Donatellis have $85,000 in cash on hand. If the funds are used to purchase a deferred annuity from a life insurance company providing a rate of return of 8.25% compounded annually, what payments will they receive at the end of every six months for 20 years after a 9-year deferral period?

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Short Answer

Q 69Q 69

$10,000 was invested in a fund earning 7.5% compounded monthly. How many monthly withdrawals of $300 can be made if the first occurs 3½ years after the date of the initial investment? Count the final smaller withdrawal.

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Short Answer

Q 70Q 70

Nancy borrowed $8,000 from her grandfather to buy a car when she started college. The interest rate being charged is only 4.5% compounded monthly. Nancy is to make the first $200 monthly payment on the loan three years after the date of the loan. How long after the date of the initial loan will she make the final payment?

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Short Answer

Q 71Q 71

A property development company obtained a $2.5 million loan to construct a commercial building. The interest rate on the loan is 5% compounded semi-annually. The lender granted a period of deferral until rental revenues become established. The first quarterly payment of $100,000 is required 21 months after the date of the loan. How long after the date of the original loan will the last payment be made?

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Essay

Q 72Q 72

Mrs. O'Reilly donated $500,000 to Medicine Hat College for a perpetual scholarship fund for women in business studies. What amount can be awarded on each anniversary if the scholarship fund earns 4½% compounded annually?

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Short Answer

Q 73Q 73

What amount is required to fund a perpetuity that pays $10,000 at the beginning of each quarter? The funds can be invested to earn 5% compounded quarterly.

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Short Answer

Q 74Q 74

A perpetuity is to pay $10,000 at the end of every six months. How much less money is required to fund the perpetuity if the money can be invested to earn 5% compounded semi-annually?

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Short Answer

Q 75Q 75

How much more money is required to fund an ordinary perpetuity than a 30-year ordinary annuity if both pay $5,000 quarterly and money can earn 5% compounded quarterly?

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Short Answer

Q 76Q 76

Ranger Oil recently donated $750,000 to the Northern Alberta Institute of Technology (NAIT) to fund (in perpetuity) five annual bursaries for students in Petroleum Engineering Technology. If the first five bursaries are to be awarded immediately, what is the maximum amount of each bursary? Assume that the bursary fund earns 4.9% compounded semi-annually.

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Short Answer

Q 77Q 77

An old agreement requires a town to pay $500 per year in perpetuity to the owner of a parcel of land for a water-well dug on the property in the 1920s. The well is no longer used, and the town wants to buy out the contract, which has become an administrative nuisance. What amount (including the regular scheduled payment) should the landowner be willing to accept on the date of the next scheduled payment if long-term low-risk investments now earn 3.8% compounded annually?

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Short Answer

Q 78Q 78

A city sells plots in its cemetery for $1,000 plus an amount calculated to provide for the cost of maintaining the grounds in perpetuity. This cost is figured at $25 per plot due at the end of each quarter. If the city can invest the funds to earn 4.8% compounded annually in perpetuity, what is the price of a plot?

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Q 79Q 79

Mr. O'Connor set up a trust account paying $500 per month in perpetuity to the local hospital. These payments consume all the interest earned monthly by the trust. Between what amounts does the balance in the trust account fluctuate if it earns 6% compounded monthly?

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Q 80Q 80

If money can earn 6% compounded annually, what percentage more money is required to fund an ordinary perpetuity paying $1,000 at the end of every year than to fund an ordinary annuity paying $1,000 per year for 25 years?

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Q 81Q 81

How much more money is required to fund an ordinary perpetuity than a 25-year ordinary annuity if the funds can earn 7% compounded quarterly and both pay $500 monthly?

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Q 82Q 82

Dr. Pollard donated $100,000 to the Canadian National Institute for the Blind. The money is to be used to make semi-annual payments in perpetuity (after a period of deferral) to finance the recording of books on tape. The first perpetuity payment is to be made five years from the date of the donation. If the funds are invested at 5% compounded semi-annually, what will be the size of the payments?

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Q 83Q 83

Mr. Larsen's will directed that $200,000 be invested to establish a perpetuity making payments at the end of each month to his wife for as long as she lives and subsequently to the Canadian Heart Foundation. What will the payments be if the funds can be invested to earn 5.4% compounded monthly?

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Q 84Q 84

Mrs. McTavish wants to establish an annual $5,000 scholarship in memory of her husband. The first scholarship is to be awarded two years from now. If the funds can earn 6.25% compounded annually, what amount must Mrs. McTavish pay now to sustain the scholarship in perpetuity?

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Q 85Q 85

What percentage more money is required to fund an ordinary perpetuity than to fund a 30-year ordinary annuity if the funds can earn 5.8% compounded semi-annually? The perpetuity and the annuity each pay $1,000 semi-annually.

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Q 86Q 86

The common shares of Unicorp. are forecast to pay annual dividends of $2 at the end of each of the next five years, followed by dividends of $3 per year in perpetuity. What is the fair market value of the shares if the market requires a 8% annually compounded rate of return on shares having a similar degree of risk?

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Q 87Q 87

Mr. Chan has donated $1 million to a college to set up a perpetuity for the purchase of books and journals for a new library to be built and named in his honour. The donation will be invested and earnings will compound for three years, at which time the first of the quarterly perpetuity payments will be made. If the funds earn 6% compounded quarterly, what will be the size of the payments?

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Q 88Q 88

A wealthy benefactor has donated $1,000,000 to establish a perpetuity that will be used to support the operating costs of a local heritage museum scheduled to open in 3 years' time. If the funds earn 4.8% compounded monthly, what monthly payments, the first occurring three years from now, can the museum expect?

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Q 89Q 89

A legal dispute delayed for 18 months the disbursement of a $500,000 bequest designated to provide quarterly payments in perpetuity to a hospice. While under the jurisdiction of the court, the funds earned interest at the rate of 5% compounded semi-annually. The hospice has just invested the $500,000 along with its earnings in a perpetual fund earning 5.2% compounded semi-annually. What payments will the hospice receive beginning three months from now?

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Q 90Q 90

The common shares of Bancorp Ltd. are forecast to pay annual dividends of $3 at the end of each of the next five years, followed by dividends of $2 per year in perpetuity. What is the fair market value of the shares if the market requires a 5% annually compounded rate of return on shares having a similar degree of risk?

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Q 91Q 91

Suppose year-end contributions to an RRSP start at $3,000 and increase by 2.5% per year thereafter. What will be the amount in the RRSP after 25 years if the plan earns 9% compounded annually?

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Q 92Q 92

Randall wants to accumulate $750,000 in his RRSP by the end of his 30-year working career. What should be his initial year-end contribution if he intends to increase the contribution by 3% every year and the RRSP earns 5.25% compounded annually?

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Q 93Q 93

How much will it cost to purchase a 20-year indexed annuity in which the end-of-quarter payments start at $5,000 and grow by 2% compounded quarterly? Assume that the money used to purchase the annuity earns 6% compounded quarterly.

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Q 94Q 94

Ken Tuckie is about to buy a 25-year annuity that will deliver end-of-month payments. The first payment will be $1,000. How much more will it cost to index the annuity so that payments grow at the rate of 2.4% compounded monthly? Assume the money used to purchase the annuity earns 5.4% compounded monthly.

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Q 95Q 95

Ida Ho is about to retire from a government job with a pension that is indexed to the Consumer Price Index (CPI). She is 60 years old and has a life expectancy of 25 years. Estimate the current economic value of her pension which will start at $20,000 per year? For the purpose of this estimation, assume that Ida will draw the pension for 25 years, the annual pension will be paid in a single year-end payment, the CPI will rise 2.5% per year, and money is worth 5% compounded annually. How much of the current economic value comes from indexing?

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Q 96Q 96

Dean has already implemented the first stage of his financial plan. Over a 30-year period, he will continue to increase his annual year-end RRSP contributions by 2% per year. His initial contribution was $2,000. At the end of the 30 years, he will transfer the funds to an RRIF and begin end-of-month withdrawals that will increase at the rate of 1.8% compounded monthly for 25 years. Assume that his RRSP will earn 6% compounded annually and his RRIF will earn 3% compounded monthly. What will be the size of his initial RRIF withdrawal?

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Q 97Q 97

In this LO, does constant growth mean that each successive payment increases by the same dollar amount? If not, what does it mean?

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Q 98Q 98

The dividends on the common shares of Mosco Inc. are forecast to grow at 10% per year for the next five years. Thereafter, the best guess is that the annual dividend will grow at the same 3% annual rate as the nominal GNP. A $2.00 dividend for the past year was recently paid. Assume that the required rate of return is 9% compounded annually. What is the fair market value of the shares if we ignore all dividends beyond a 30-year time horizon?

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Q 99Q 99

Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 100Q 100

Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 101Q 101

Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 102Q 102Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 103Q 103Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 104Q 104Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 105Q 105Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 106Q 106Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 107Q 107Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 108Q 108

Determine the periodic payment for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 109Q 109

Determine the periodic payment for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 110Q 110

Determine the periodic payment for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 111Q 111Determine the periodic payment for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 112Q 112Determine the periodic payment for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 113Q 113Determine the periodic payment for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 114Q 114

Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 115Q 115

Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 116Q 116

Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 117Q 117Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 118Q 118Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 119Q 119Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

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Q 120Q 120

What price will a finance company pay to a merchant for a conditional sale contract that requires 15 monthly payments of $231 beginning in six months? The finance company requires a rate of return of 18% compounded monthly.

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Q 121Q 121

What price will a finance company pay to a merchant for a conditional sale contract that requires 12 monthly payments of $249, with the first payment due six months from now? The finance company requires a return of 16.5% compounded monthly.

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Q 122Q 122

What amount must be invested today to allow for quarterly payments of $2,500 at the end of every quarter for 15 years after a six-year deferral period? Assume that the funds will earn 5% compounded semi-annually.

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Q 123Q 123

Harold, just turned 27, wants to accumulate an amount in his RRSP at age 60 that will have the purchasing power of $300,000 in current dollars. What annual contributions on his 28

^{th}through 60^{th}birthdays are required to meet this goal if the RRSP earns 8.5% compounded annually and the rate of inflation is 2.5% per year?Free

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Q 124Q 124

As of Brice's 54

^{th}birthday, he has accumulated $154,000 in his Registered Retirement Savings Plan (RRSP). What size of end-of-month payments in a 20-year annuity will these funds purchase at age 65 if he makes no further contributions? Assume that his RRSP and the investment in the annuity will earn 8.25% compounded monthly.Free

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Q 125Q 125

Leslie received a $40,000 settlement when her employer declared her job redundant. Under special provisions of the Income Tax Act, she was eligible to place $22,000 of the amount in an RRSP. Fifteen years from now, she intends to transfer the money from the RRSP to a Registered Retirement Income Fund (RRIF). Thereafter, Leslie will make equal withdrawals at the end of each quarter for 20 years. If both the RRSP and the RRIF earn 8.5% compounded quarterly, what will be the amount of each withdrawal?

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Q 126Q 126

Fred asked two life insurance companies to give quotes on a 20-year deferred annuity (after a 5-year deferral period) that can be purchased for $100,000. Northwest Mutual quoted payments of $875 payable at the end of each month. Liberty Standard stated that all their annuity options provide a rate of return equal to 5.5% compounded annually. Which should Fred choose?

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Q 127Q 127

$30,000 is placed in a fund earning 7% compounded quarterly. How many quarterly withdrawals of $2,000 can be made if the first withdrawal occurs three years from today? Count the final withdrawal, which will be less than $2,000.

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Q 128Q 128Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 129Q 129Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 130Q 130Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

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Q 131Q 131

The Bay is offering "no money down, and no payments for a year." The total cost of a purchase of electronic equipment is $3500 including taxes. What monthly payment is required to pay off this debt in two years, if payments start in one year, and the Bay charges interest at 2% per month? What is the amount of interest that the purchaser pays overall?

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Q 132Q 132

A finance company paid a merchant $3,975 for a conditional sale contract after discounting it to yield 18% compounded monthly. If the contract is for 20 monthly payments of $256.96 following a payment-free period, what is the time interval between the date of sale and the first payment?

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Q 133Q 133

To sell a farm that it had acquired in a foreclosure action, the Royal Bank agreed to monthly payments of $2,700 for 20 years, with the first payment due 15 months from the date of sale. If the purchaser paid 15% down and the interest rate on the balance is 9% compounded annually, what was the purchase price?

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Q 134Q 134

How long (before the first withdrawal) must a $19,665 investment earning 9.5% compounded semi-annually be allowed to grow before it can provide 60 quarterly withdrawals of $1,000?

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Q 135Q 135

Duncan retired recently and plans to utilize other savings for a few years while his RRSP continues to grow on a tax-deferred basis. The RRSP is currently worth $142,470. How long will it be until the amount in the RRSP is large enough to purchase a 25-year annuity paying $1700 at the end of each month? Assume that the RRSP and the annuity will earn 8.75% compounded semi-annually.

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Q 136Q 136

What is the current economic value of an inheritance that will pay $2,500 to the beneficiary at the beginning of every three months for 20 years starting when the beneficiary reaches 21 years of age, 5¼ years from now? Assume that money can earn 6% compounded monthly.

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Q 137Q 137

Mrs. Clare wants to set up a college fund for her daughter so that she will have a monthly income of $500 each month for three years starting 10 years from now. How much should she deposit today if money earns 4.25% compounded monthly?

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Q 138Q 138

What amount invested today will provide yearly payments of $50,000 for 20 years starting 10 years from now if invested at 5.5% compounded annually?

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Q 139Q 139

What is the current economic value of an inheritance that will pay $2,500 to the beneficiary at the beginning of every three months for 20 years starting when the beneficiary reaches 21 years of age, 5¼ years from now? Assume that money can earn 6% compounded monthly.

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Q 140Q 140

A $30,000 loan bearing interest at 9% compounded monthly was repaid, after a period of deferral, by monthly payments of $425.10 for 10 years. What was the time interval between the date of the loan and the first payment?

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Q 141Q 141

Mr. Parmar wants to retire in 20 years and purchase a 25-year annuity that will make equal payments at the end of every quarter. The first payment should have the purchasing power of $6,000 in today's dollars. If he already has $54,000 in his RRSP, what contributions must he make at the end of every half-year for the next 20 years to achieve his retirement goal? Assume that the rate of inflation for the next 20 years will be 2.5%, the RRSP will earn 8% compounded semi-annually, and the rate of return on the fund from which the annuity is paid will be 5.5% compounded quarterly.

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Q 142Q 142

Mrs. Henry wants to receive payments of $1,000 per month for 20 years when she retires in 15 years. She wants to know how much she should deposit into an account today to reach her goal if money is worth 5.75% compounded quarterly?

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Q 143Q 143

Mrs. Clare left $150,000 to her local college for an annual scholarship for students in need. What is the amount of the scholarship if the fund earns 3.75% compounded annually?

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Q 144Q 144

What is the fair market value of a perpetual preferred share just after the semi-annual dividend of $.60 has been paid if shares of similar risk are earning 7.25% compounded semi-annually?

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Q 145Q 145

A retiree of the local college has asked that any money collected for a retirement gift be used to set up a perpetuity scholarship fund for a third-year student in the School of Business. A total of $3750 was collected. If interest earns 4% compounded annually, what will be the amount of the yearly scholarship?

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Q 146Q 146

What semi-annual compounded nominal rate of return is required to return $5,000 every six months if the perpetuity fund is $265,000?

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Q 147Q 147

Sam wants to set up scholarships for his former secondary school graduating class. He has invested $100,000 into an account that pays 4.5% compounded quarterly. If the scholarships are $1,500 each and presented annually at graduation, how many scholarships can be awarded each year?

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Q 148Q 148

A business group is considering establishing an endowment to allow eligible employees an opportunity to further their education. The amount of the grant available will be $10,000 per month. If the amount the business group is investing is $2 million, what nominal rate of return must the investment earn to fully fund the grant?

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Q 149Q 149

What is the fair market value of a perpetual preferred share just after the quarterly dividend of $1.40 has been paid if shares of similar risk are earning 5.5% compounded annually?

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Q 150Q 150

What quarterly compounded nominal rate of return is required to return $2,000 per quarter if the perpetuity fund is $98,000? What is the effective rate of interest?

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Q 151Q 151

The fair market value of a preferred share is $45. The share pays a quarterly payment of $.65. An investor is able to purchase the share for $42. What will be the investor's annually compounded rate of return?

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Q 152Q 152

What amount must be placed in a perpetual fund today if the fund earns 3.75% compounded quarterly, and payments of $1,000 are to be made monthly, starting one month from today?

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Q 153Q 153

As an employee benefit, a company has offered a fund of $750,000 for eligible children of employees to receive a scholarship of $2,500 per year for post-secondary education. If interest earns 4% compounded annually, how many scholarships can be provided per year?

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Q 154Q 154

What amount must be placed in a perpetual fund today if the fund earns 4.25% compounded semi-annually, and payments of $2500 are to be made monthly, starting two years from today?

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Q 155Q 155

Mrs. Lyons has deposited $175,000 at 5.25% compounded quarterly. In 10 years, she plans to convert the accumulated amount into a perpetuity, in which she will receive the same amount at the end of each month. What is the maximum payment she can receive if the interest rate stays the same?

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Q 156Q 156

Mrs. Hunking wants to set up a fund so that she will receive $2500 at the end of each quarter starting in 20 years, but leave the principal amount untouched. If interest is 4.25% compounded semi-annually, how much would she have to deposit today to reach her goal?

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Q 157Q 157

What amount today will provide payments of $1,500 at the end of each month starting in 10 years, if the principal amount is to remain untouched, and money can earn 4.85% compounded quarterly?

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Q 158Q 158

An investment of $100,000 at 4.75% compounded semi-annually was made so that in 20 years, it can be converted into a perpetuity, which will pay the same amount at the end of each month. What is the maximum payment the investment can pay?

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Q 159Q 159

Year-end contributions to an RRSP start at $1,200 and increase each year by 4% thereafter. What amount will be in the RRSP account after 20 years if money earns 5% compounded annually?

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Q 160Q 160

Jack is 25 years old. He has deposited $1,000 into an RRSP fund, and plans to deposit $1,000 plus an additional 5% each year until he retires at age sixty-five. How much will Jack have in his RRSP account when he retires if money earns 4.75% compounded annually?

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Q 161Q 161

Erica is making contributions to her RRSP by depositing an initial $1,500 at the end of December this year, and then increasing the deposit by 8% each year after. What will be the amount of her deposit in the twentieth year?

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Q 162Q 162

How much will it cost to buy a 20-year monthly annuity that grows at 2.5% compounded monthly, if the first payment is $1,500 and money is worth 4.25% compounded monthly?

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Q 163Q 163

How much will it cost to buy a 30-year quarterly annuity that grows at 2% compounded quarterly, if the first payment is $3,000 and money is worth 4% compounded quarterly?

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Q 164Q 164

Marika wants to have $500,000 in her RRSP account in 40 years. Money currently earns 4.25% compounded annually, and Marika plans to make contributions to her RRSP account at the end of each year increased each time by 3% to adjust for inflation. What will be Marika's initial contribution?

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Q 165Q 165

What is the amount of the initial deposit required to have an RRSP account of $1 million in 30 years, if deposits are made at the end of each month, the plan allows for a 2% adjustment for inflation, and money earns 4% compounded monthly?

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Q 166Q 166

What is the amount of the initial deposit required to have an RRSP account of $750,000 in 40 years, if deposits are made at the end of each quarter, the plan allows for a 2.5% adjustment for inflation, and money earns 3.8% compounded quarterly?

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Q 167Q 167

Marion wants to buy an investment that will pay her $2,000 for the first month, and include a 3% growth rate compounded monthly for each subsequent monthly payment. The term of the investment is for 25 years, and Marion wants to start receiving the payments 10 years from now. What amount should she deposit today to reach her goal if the investment can earn 6% compounded monthly?

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