Question 1

What is the present value of $300 received at the beginning of each year for five years? Assume that the first payment is not received until the beginning of the third year (thus the last payment is received at the beginning of the seventh year).Use a 10% discount rate,and round your answer to the nearest $100.
A)$1,100
B)$1,000
C)$900
D)$1,200

Accepted Answer

B

Question 2

When comparing annuity due to ordinary annuities,annuity due annuities will have higher
A)present values.
B)annuity payments.
C)future values.
D)both A and C.
E)all of the above.

Accepted Answer

An annuity due is a type of annuity where payments are made at the beginning of each period, while in an ordinary annuity, payments are made at the end of each period. Since the payments in an annuity due occur one period earlier than in an ordinary annuity, the present value of an annuity due will be higher than that of an ordinary annuity because of the time value of money. Similarly, the future value of an annuity due will also be higher than that of an ordinary annuity due to the additional compounding of interest for one extra period. Therefore, both the present value and future value of an annuity due will be higher than those of an ordinary annuity, making choice D the correct answer.

Question 3

Francis Peabody just won the $89,000,000 Oz Lotto prize.The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year.Assume that funds would be invested at 7.65%.Francis is trying to decide whether to take the lump sum or the annual installments.What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.
A)$89,000,000
B)$38,163,612
C)$13,092,576
D)$41,083,128

Accepted Answer

The present value of an annuity formula is used to calculate the lump sum equivalent of the annual installments. Using the formula with a 7.65% interest rate over 26 years, the present value is approximately $41,083,128.

Question 4

What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%.The first payment will be received one year from today (round to the nearest $1).
A)$42
B)$114
C)$88
D)$105

Accepted Answer

The answer of What is the present value of $27...

Question 5

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today,and the discount rate is 10% (round to nearest $10).
A)$120
B)$130
C)$100
D)$110

Accepted Answer

Using the formula for the present value of an annuity:
PV = (C * (1 - (1+r)^-n)) / r
PV = (27 * (1 - (1+0.1)^-6)) / 0.1
PV = $130.05
Rounding to the nearest $10 gives the answer of $130, which is option B.

Question 6

Your company has received a $50,000 loan from an industrial finance company.The annual payments are $6,202.70.If the company is paying 9% interest per year,how many loan payments must the company make?
A)15
B)13
C)12
D)19

Accepted Answer

The number of loan payments can be found using the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (loan amount), PMT is the annual payment, r is the annual interest rate, and n is the number of payments. Rearranging the formula to solve for n gives: $n = \frac{\log(1 - \frac{PV \times r}{PMT})}{\log(1 + r)}$. Substituting the given values ($PV = 50,000$, $PMT = 6,202.70$, $r = 0.09$) into the formula and solving for n yields approximately 15 payments.

Question 7

If you invest $750 every six months at 8% compounded half-yearly,how much would you accumulate at the end of 10 years?
A)$10,065
B)$10,193
C)$22,334
D)$21,731

Accepted Answer

The future value of an annuity formula is used: FV = P * [(1 + r)^nt - 1] / r, where P = $750, r = 0.08/2, n = 2, t = 10. Plugging in the values gives the accumulated amount.

Question 8

You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12.The annual interest rate is
A)24%.
B)8%.
C)18%.
D)12%.

Accepted Answer

The answer of You wish to borrow $2,000 to be...

Question 9

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10).The discount rate is 13%.To solve this problem with a financial calculator,the correct choice is
A)N=7,i=13,PMT= 100,FV=0,solve for PV
B)N=7,i=13,PV= 100,FV=0,solve for FV
C)N=7,i=13,PMT= 100,FV=100,solve for PV
D)N=7,i=.13,PMT= 100,FV=0,solve for PV

Accepted Answer

We need to find the present value of an annuity, therefore we are solving for PV. The payment is $100 received at the end of each year, therefore PMT = 100. The annuity is for seven years, therefore N = 7. The discount rate is 13%, therefore i = 13. The future value is not given but is not relevant for this problem, therefore FV = 0. Thus, we use the formula PV = PMT x ((1 - (1 + i)^-n) / i) and input the values into a financial calculator or spreadsheet program to get the answer. The correct choice is A.

Question 10

Ingrid Birdman can earn a nominal annual rate of return of 12%,compounded semiannually.If Ingrid made 40 consecutive semiannual deposits of $500 each,with the first deposit being made today,how much will she accumulate at the end of Year 20? Round off to the nearest $1.
A)$52,821
B)$57,901
C)$82,024
D)$64,132

Accepted Answer

There are two key pieces of information in this problem: Ingrid makes 40 semiannual deposits of $500 each, and she earns a nominal annual rate of return of 12%, compounded semiannually.

To calculate how much Ingrid will accumulate at the end of 20 years, we need to use the formula for the future value of an annuity:

FV = Pmt x (((1 + r/n)^(n*t)) - 1) / (r/n)

where:
- Pmt is the payment per period (in this case, $500)
- r is the nominal annual rate of return (12%)
- n is the number of compounding periods per year (2, since the interest is compounded semiannually)
- t is the total number of periods (in this case, 40 semiannual periods over 20 years)

Plugging in the numbers, we get:

FV = $500 x (((1 + 0.12/2)^(2*40)) - 1) / (0.12/2)
FV = $500 x (1.12^80 - 1) / 0.06
FV = $500 x 276.972
FV = $138,486

However, this is the future value of Ingrid's deposits PLUS the interest earned on those deposits. Since she only deposited a total of $20,000 ($500 x 40), we need to subtract that to find the amount of interest earned:

$138,486 - $20,000 = $118,486

So Ingrid will accumulate $118,486 at the end of 20 years, rounded to the nearest dollar. The closest answer choice is C) $82,024, so the correct answer is C).

Question 11

What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today.Use a discount rate of 9%,and round your answer to the nearest $10.
A)$1,360
B)$1,480
C)$1,250
D)$1,210

Accepted Answer

The answer of What is the present value of $150...

Question 12

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%.The first payment will be received one year from today (round to the nearest $1).
A)$25
B)$40
C)$57
D)$118

Accepted Answer

Using the formula for the present value of an annuity:
PV = [C(1 - (1+r)^-n)] / r
where C = the annual cash flow ($12 in this case), r = the discount rate (11%), and n = the number of periods (7 years).
Plugging in the values, we have:
PV = [12(1 - (1+0.11)^-7)] / 0.11
PV = $57.41
Rounding to the nearest dollar, the answer is $57, which corresponds to choice C.

Question 13

A commercial bank will loan you $7,500 for two years to buy a car.The loan must be repaid in 24 equal monthly payments.The annual interest rate on the loan is 12% of the unpaid balance.What is the amount of the monthly payments?
A)$282.43
B)$390.52
C)$369.82
D)$353.05

Accepted Answer

The answer of A commercial bank will loan you $7,500...

Question 14

Gina Dare,who wants to be a millionaire,plans to retire at the end of 40 years.Gina's plan is to invest her money by depositing into her Superannuation account.What is the amount that she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will earn an annual rate of 11.5%.Round off to the nearest $1.
A)$1,497
B)$5,281
C)$75
D)$3,622

Accepted Answer

The correct answer is A.The formula for calculating the annual deposit required to accumulate a future value is:PMT = FV * (r / ((1 + r)^n - 1))where:PMT = annual depositFV = future valuer = annual interest raten = number of yearsIn this case, we have:FV = $1,000,000r = 11.5% = 0.115n = 40Plugging these values into the formula, we get:PMT = $1,000,000 * (0.115 / ((1 + 0.115)^40 - 1))PMT = $1,000,000 * (0.115 / 105.317)PMT = $1,000,000 * 0.00114PMT = $1,497Therefore, Gina needs to deposit $1,497 annually in order to accumulate $1,000,000 in her Superannuation account.

Question 15

As time increases for an amortised loan,the ________ decreases.
A)interest paid per payment
B)principal paid per payment
C)the outstanding loan balance
D)both A and C

Accepted Answer

In an amortized loan, the amount of interest paid per payment decreases over time as the outstanding loan balance decreases with each payment. Therefore, we can eliminate choices A and B. The correct answer is D, as both A and C are true statements about how an amortized loan works.

Question 16

If you have $20,000 in an account earning 8% annually,what constant amount could you withdraw each year and have nothing remaining at the end of five years?
A)$3,525.62
B)$5,008.76
C)$3,408.88
D)$2,465.78

Accepted Answer

The answer of If you have $20,000 in an account...

Question 17

It is January 1st and Jeff Davis has just established a Superannuation account.Jeff will put $1,000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total).How much money will Jeff have in his account at the beginning of the 41st year? Assume that the account pays 12% interest compounded annually,and round to the nearest $1,000.
A)$93,000
B)$766,000
C)$767,000
D)$850,000

Accepted Answer

This is a case of a regular annuity since Jeff will be depositing the same amount at the end of every year. Using the formula for regular annuities, we have:
PMT = $1,000
r = 12% = 0.12
n = 40 (number of years)
Using the formula for future value of a regular annuity, we have:
FV = PMT * ((1 + r)^n - 1) / r
FV = $1,000 * ((1 + 0.12)^40 - 1) / 0.12
FV = $766,470.74
Rounding to the nearest $1,000, Jeff will have $767,000 in his account at the beginning of the 41st year. Therefore, the answer is C.

Question 18

________ annuities involve depositing money at the end of the period and allowing it to grow.
A)Discount
B)Ordinary
C)Annuity due
D)Both B and C

Accepted Answer

Ordinary annuities involve depositing money at the end of the period and allowing it to grow. Annuity due involves depositing money at the beginning of the period. Discount annuities are the opposite of ordinary annuities, where the future value is known and the present value needs to be calculated. Therefore, the correct choice is option B.

Question 19

What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today.Use a discount rate of 12%,and round your answer to the nearest $10.
A)$1,870
B)$2,090
C)$2,117
D)$3,243

Accepted Answer

To find the present value, we need to use the formula: 
PV = PMT [(1 - (1/(1+r)^n))/r],
where PV is the present value, PMT is the annuity payment, r is the discount rate, and n is the number of periods.

Substituting in the given values, we get:
PV = $250 [(1 - (1/(1+0.12)^21))/0.12]
PV = $2,117.34

Rounding to the nearest $10, the present value is $2,120, so the best answer is C.

Question 20

Charlie Stone wants to retire in 30 years,and he wants to have an annuity of $1,000 a year for 20 years after retirement.Charlie wants to receive the first annuity payment at the end of the 30th year.Using an interest rate of 10%,how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?
A)$500
B)$490
C)$540
D)$570

Accepted Answer

To calculate the present value of an annuity, we need to use the formula:

PV = A * (1 - (1 / (1 + r)^n)) / r

Where PV is the present value, A is the annuity payment, r is the interest rate, and n is the number of payments.

In this case, Charlie wants to receive an annuity of $1,000 a year for 20 years after he retires in 30 years. So, the number of payments n is 20, and the first payment comes at the end of the 30th year, so we need to discount it back 30 years to calculate the present value.

r = 10% or 0.1
n = 20
A = $1,000

PV = $1,000 * (1 - (1 / (1 + 0.1)^20)) / 0.1 * (1 + 0.1)^-30
PV = $540.17

Therefore, Charlie needs to invest $540.17 today to have an annuity of $1,000 for 20 years after he retires in 30 years. Rounded to the nearest $10, the answer is $540.

Quiz 6: The Time Value of Money - Annuities and Other Topics

When comparing annuity due to ordinary annuities,annuity due annuities will have higher

What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%.The first payment will be received one year from today (round to the nearest $1) .

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today,and the discount rate is 10% (round to nearest $10) .

Your company has received a $50,000 loan from an industrial finance company.The annual payments are $6,202.70.If the company is paying 9% interest per year,how many loan payments must the company make?

If you invest $750 every six months at 8% compounded half-yearly,how much would you accumulate at the end of 10 years?

You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12.The annual interest rate is

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10) .The discount rate is 13%.To solve this problem with a financial calculator,the correct choice is

Ingrid Birdman can earn a nominal annual rate of return of 12%,compounded semiannually.If Ingrid made 40 consecutive semiannual deposits of $500 each,with the first deposit being made today,how much will she accumulate at the end of Year 20? Round off to the nearest $1.

What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today.Use a discount rate of 9%,and round your answer to the nearest $10.

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%.The first payment will be received one year from today (round to the nearest $1) .

A commercial bank will loan you $7,500 for two years to buy a car.The loan must be repaid in 24 equal monthly payments.The annual interest rate on the loan is 12% of the unpaid balance.What is the amount of the monthly payments?

As time increases for an amortised loan,the ________ decreases.

If you have $20,000 in an account earning 8% annually,what constant amount could you withdraw each year and have nothing remaining at the end of five years?

________ annuities involve depositing money at the end of the period and allowing it to grow.

What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today.Use a discount rate of 12%,and round your answer to the nearest $10.