Question 1

How many more RRSP contributions of $300 at the beginning of every month are required to reach $200,000 if the funds earn 6.75% compounded monthly than if they earn 8.5% compounded monthly?

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Question 2

As of the date of Colony Farm's most recent financial statements, 3½ years remained in the term of a capital lease reported as a long-term liability of $27,400. If the beginning-of-month lease payments are $750, what monthly compounded nominal (annual) discount rate was used in valuing the lease?

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Question 3

If a furniture store offers to sell a washer-dryer combination priced at $1395 on a conditional sale contract requiring 12 monthly payments of $125 (including a payment on the date of sale), what effective rate of interest is being charged?

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Question 4

Sovereign Life Insurance Company of Canada offers $250,000 of term life insurance to a 45-year-old male for an annual premium of $716 (in advance) or for monthly premium payments (in advance) of $62.50 by preauthorized cheques. What effective rate of interest is charged to those who pay monthly?

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Question 5

Fred is about to have his 27^th birthday. He has set a goal of retiring at age 58 with $1,000,000 in his RRSP. For planning purposes, he is assuming that his RRSP will earn 8% compounded annually. a) What contributions on each birthday from age 27 to 57 inclusive will be required to accumulate the desired amount in his RRSP? b) If he waits five years before starting his RRSP, what contributions on each birthday from age 32 to 57 inclusive will be required to reach the target?

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Question 6

What is the initial economic value of an annuity due if it consists of 19 semiannual payments of $1500? Money is worth 5% compounded semiannually for the first five years and 10% compounded semiannually thereafter.

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Question 7

What will be the amount in an RRSP after 30 years if contributions of $4000 are made at the beginning of each year for the first 10 years, and contributions of $6000 are made at the beginning of each year for the subsequent 20 years? Assume that the RRSP will earn 8.25% compounded annually.

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Question 8

Calculate the future value of an investment plan requiring contributions of $800 at the beginning of each calendar quarter for seven years. Assume that the rate of return will be 8% compounded quarterly for the first 30 months and 7% compounded semiannually for the remainder of the annuity's term.

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Question 9

Ms. Bowers wants to be able to purchase a 20-year annuity at age 62 that will pay her $3500 at the beginning of each month. She makes her first quarterly contribution to an RRSP on her 35^th birthday and continues them up to but not including her 62^nd birthday. What should be the amount of each contribution? Assume that her RRSP will earn 8% compounded quarterly and that the money used to purchase the annuity fund will earn 4.8% compounded monthly.

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Question 10

Mr. and Mrs. Zolob contributed $50 on the first of each month to an RESP they set up for their grandson Jeff. By the time he entered Mohawk College, 14 years and 5 months of contributions had accumulated. The grandparents' contributions stopped, and Jeff started beginning-of-month withdrawals of $500.
 How long will these payments last if the RESP has earned and will continue to earn 8.25% compounded monthly?

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Question 11

A rental agreement requires the payment of $1000 at the beginning of each month.
a) What single payment at the beginning of the rental year should the landlord accept instead of monthly payments if money is worth 8% compounded monthly?
b) Show that the landlord will be equally well off at the end of the year under either payment arrangement if rental payments are invested at 8% compounded monthly.

Accepted Answer

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Question 12

Mick contributed $5000 at the beginning of each year for 25 years to his RRSP. Assume that the RRSP earned 8% compounded annually. What percentage of the RRSP's value after 25 years comes from contributions made in the first five years?

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Question 13

What amount is required to purchase an annuity that pays $4000 at the end of each quarter for the first five years and then pays $2500 at the beginning of each month for the subsequent 15 years? Assume that the annuity payments are based on a rate of return of 5.6% compounded quarterly.

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Question 14

Suppose that $5000 is contributed at the beginning of each year for 25 years to an RRSP that earns 10% compounded annually. By what percentage would annual contributions have to be increased in order to have the same future value after 25 years if the plan earns only 8% compounded annually?

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Question 15

Suppose you contribute $2500 to an RRSP at the beginning of every six months for 25 years, and then use the accumulated funds to purchase an annuity paying $2500 at the beginning of each month. How long after the start of the annuity will the last payment be made? Assume that the RRSP earns 8% compounded semiannually and the funds invested in the annuity earn 5.1% compounded monthly.

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Question 16

Capital Leasing leases commercial kitchen equipment to restaurants, hotels, hospitals, and other institutions. Capital Leasing calculates the payments on its four year leases so that it recovers the purchase price of the equipment plus a return on investment of 16% compounded annually over the term of the lease. What will be the required lease payments at the beginning of each quarter on equipment purchased by Capital for $57,000?

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Question 17

New Look Fitness Centre offers a one-year membership for $500 in advance or a three month membership for $160 in advance. What effective rate of interest is an individual paying if she buys four consecutive three month memberships instead of a one year membership?

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Question 18

A life insurance company is calculating the monthly premium that it will offer clients as an alternative to paying the full annual premium. With both alternatives, premiums are payable at the beginning of the period of coverage. If the monthly payment by preauthorized cheque is calculated to yield the insurance company 10% compounded semiannually on the unpaid balance of the annual premium, what should be the monthly premium per $100 of annual premium?

Accepted Answer

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Question 19

Mandeep is depositing $250 at the beginning of each month into an RRSP account paying 3.8% compounded monthly. How much will she have in her RRSP account after 40 years?

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Question 20

Larissa is depositing $1000 at the beginning of each quarter into an RRSP account paying 4.25% compounded semiannually. How much will she have in her RRSP account after 30 years?

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Quiz 12: Annuities Due