Question 1

How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?

Accepted Answer

A)  $3,604.78 
B)  $3,746.25 
C)  $4,037.35 
D) $4,604.78 
A)  $3,604.78 
B)  $3,746.25 
C)  $4,037.35 
D) $4,604.78

Question 2

Which one of the following will increase the present value of an annuity, other things equal?

Accepted Answer

A)  Increasing the interest rate 
B)  Decreasing the interest rate 
C)  Decreasing the number of payments 
D) Decreasing the amount of the payment 
A)  Increasing the interest rate 
B)  Decreasing the interest rate 
C)  Decreasing the number of payments 
D) Decreasing the amount of the payment

Question 3

Converting an annuity to an annuity due decreases the present value.

Accepted Answer

A) True 
 B)False

Question 4

What is the minimum nominal rate of return that you should accept if you require a 4% real rate of return and the rate of inflation is expected to average 3.5% during the investment period?

Accepted Answer

A)  7.36% 
B)  7.50% 
C)  7.64% 
D) 8.01% 
A)  7.36% 
B)  7.50% 
C)  7.64% 
D) 8.01%

Question 5

An annuity due must have a present value at least as large as an equivalent ordinary annuity.

Accepted Answer

A) True 
 B)False

Question 6

An annuity factor represents the future value of $1 that is deposited today.

Accepted Answer

A) True 
 B)False

Question 7

Nominal dollars refer to the amount of purchasing power.

Accepted Answer

A) True 
 B)False

Question 8

What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be amortized over 30 years?

Accepted Answer

A)  $771.46 
B)  $775.90 
C)  $1,028.61 
D) $1,034.53 
A)  $771.46 
B)  $775.90 
C)  $1,028.61 
D) $1,034.53

Question 9

On the day you retire you have $1,000,000 saved. You expect to live another 25 years during which time you expect to earn 6.19% on your savings while inflation averages 2.5% annually. Assume you want to spend the same amount each year in real terms and die on the day you spend your last dime. What real amount will you be able to spend each year?

Accepted Answer

A)  $61,334.36 
B)  $79,644.58 
C)  $79,211.09 
D) $61,931.78 
A)  $61,334.36 
B)  $79,644.58 
C)  $79,211.09 
D) $61,931.78

Question 10

If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments, what is the annual percentage rate?

Accepted Answer

A)  4.02% 
B)  10.02% 
C)  14.50% 
D) 15.19% 
A)  4.02% 
B)  10.02% 
C)  14.50% 
D) 15.19%

Question 11

The present value of a perpetuity can be determined by:

Accepted Answer

A)  multiplying the payment by the interest rate. 
B)  dividing the interest rate by the payment. 
C)  multiplying the payment by the number of payments to be made. 
D) dividing the payment by the interest rate. 
A)  multiplying the payment by the interest rate. 
B)  dividing the interest rate by the payment. 
C)  multiplying the payment by the number of payments to be made. 
D) dividing the payment by the interest rate.

Question 12

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?

Accepted Answer

A)  5.00% 
B)  5.66% 
C)  6.00% 
D) 9.46% 
A)  5.00% 
B)  5.66% 
C)  6.00% 
D) 9.46%

Question 13

If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years with monthly payments of $965.55, how much interest is paid over the life of the loan?

Accepted Answer

A)  $120,000 
B)  $162,000 
C)  $181,458 
D) $227,598 
A)  $120,000 
B)  $162,000 
C)  $181,458 
D) $227,598

Question 14

Real interest rates:

Accepted Answer

A)  always exceed inflation rates. 
B)  can decline to zero but no lower. 
C)  can be negative, zero, or positive. 
D) traditionally exceed nominal rates. 
A)  always exceed inflation rates. 
B)  can decline to zero but no lower. 
C)  can be negative, zero, or positive. 
D) traditionally exceed nominal rates.

Question 15

What is the future value of $10,000 on deposit for 5 years at 6% simple interest?

Accepted Answer

A)  $7,472.58 
B)  $10,303.62 
C)  $13,000.00 
D) $13,382.26 
A)  $7,472.58 
B)  $10,303.62 
C)  $13,000.00 
D) $13,382.26

Question 16

Some home loans involve "points," which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if 0.5 point is charged on a $100,000 loan, the loan repayment schedule is calculated on the $100,000 loan, but the net amount the borrower receives is only $99,500. What is the effective annual interest rate charged on such a loan, assuming that loan repayment occurs over 360 months, and that the interest rate is 1% per month? (Round the monthly payment amount to 2 decimal places.)

Accepted Answer

Since the monthly payment is based on a

Question 17

The discount factor is used to calculate the present value of $1 received in year t.

Accepted Answer

A) True 
 B)False

Question 18

With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years of life expectancy, what annual annuity can be withdrawn, beginning today?

Accepted Answer

A)  $112,148.50 
B)  $120,000.00 
C)  $123,371.44 
D) $133,241.15 
A)  $112,148.50 
B)  $120,000.00 
C)  $123,371.44 
D) $133,241.15

Question 19

A dollar tomorrow is worth more than a dollar today.

Accepted Answer

A) True 
 B)False

Question 20

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest with monthly compounding?

Accepted Answer

A)  $361,526.14 
B)  $388,017.16 
C)  $402,766.67 
D) $414,008.24 
A)  $361,526.14 
B)  $388,017.16 
C)  $402,766.67 
D) $414,008.24

Exam 5: The Time Value of Money

How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?

Which one of the following will increase the present value of an annuity, other things equal?

Converting an annuity to an annuity due decreases the present value.

What is the minimum nominal rate of return that you should accept if you require a 4% real rate of return and the rate of inflation is expected to average 3.5% during the investment period?

An annuity due must have a present value at least as large as an equivalent ordinary annuity.

An annuity factor represents the future value of $1 that is deposited today.

Nominal dollars refer to the amount of purchasing power.

What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be amortized over 30 years?

If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments, what is the annual percentage rate?

The present value of a perpetuity can be determined by:

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?

If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years with monthly payments of $965.55, how much interest is paid over the life of the loan?

Real interest rates:

What is the future value of $10,000 on deposit for 5 years at 6% simple interest?

The discount factor is used to calculate the present value of $1 received in year t.

With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years of life expectancy, what annual annuity can be withdrawn, beginning today?

A dollar tomorrow is worth more than a dollar today.

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest with monthly compounding?

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Using Discounted Cash-Flow Analysis to Make Investment Decisions

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