Question 1

On January 1, 2016, your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2016?

Accepted Answer

A)  $17,419.55 
B)  $17,593.75 
C)  $17,769.68 
D)  $17,947.38 
E)  $18,126.85

Question 2

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

Accepted Answer

A) True 
 B)False

Question 3

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

Accepted Answer

A) True 
 B)False

Question 4

You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

Accepted Answer

A)  if the going rate of interest decreases from 10% to 0%, the difference between the present value of ord and the present value of due would remain constant. 
B)  the present value of ord must exceed the present value of due, but the future value of ord may be less than the future value of due. 
C)  the present value of due exceeds the present value of ord, while the future value of due is less than the future value of ord. 
D)  the present value of ord exceeds the present value of due, and the future value of ord also exceeds the future value of due. 
E)  the present value of due exceeds the present value of ord, and the future value of due also exceeds the future value of ord.

Question 5

What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?

Accepted Answer

A)  $16,806 
B)  $17,690 
C)  $18,621 
D)  $19,601 
E)  $20,633

Question 6

Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan.

Accepted Answer

A) True 
 B)False

Question 7

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

Accepted Answer

A)  bank 1; 6.1% with annual compounding. 
B)  bank 2; 6.0% with monthly compounding. 
C)  bank 3; 6.0% with annual compounding. 
D)  bank 4; 6.0% with quarterly compounding. 
E)  bank 5; 6.0% with daily (365-day) compounding.

Question 8

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?

Accepted Answer

A)  $10,155.68 
B)  $10,690.19 
C)  $11,252.83 
D)  $11,845.09 
E)  $12,468.51

Question 9

Your investment account pays 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

Accepted Answer

A)  5.14 
B)  5.71 
C)  6.35 
D)  7.05 
E)  7.84

Question 10

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.

Accepted Answer

A) True 
 B)False

Question 11

Which of the following statements is CORRECT?

Accepted Answer

A)  some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts. 
B)  a time line is not meaningful unless all cash flows occur annually. 
C)  time lines are useful for visualizing complex problems prior to doing actual calculations. 
D)  time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. 
E)  time lines cannot be constructed for annuities where the payments occur at the beginning of the periods.

Question 12

If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following statements is CORRECT?

Accepted Answer

A)  if some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity. 
B)  the cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. 
C)  if a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity. 
D)  the cash flows for an annuity due must all occur at the beginning of the periods. 
E)  the cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.

Question 14

Your aunt wants to retire and has $375,000. She expects to live for another 25 years and to earn 7.5% on her invested funds. How much could she withdraw at the end of each of the next 25 years and end up with zero in the account?

Accepted Answer

A)  $28,843.38 
B)  $30,361.46 
C)  $31,959.43 
D)  $33,641.50 
E)  $35,323.58

Question 15

Geraldine was injured in a car accident, and the insurance company has offered her the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave her as well off financially as with the annuity?

Accepted Answer

A)  $225,367 
B)  $237,229 
C)  $249,090 
D)  $261,545 
E)  $274,622

Question 16

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

Accepted Answer

A)  $4,750 
B)  $5,000 
C)  $5,250 
D)  $5,513 
E)  $5,788

Question 17

Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Accepted Answer

A)  $5,493.71 
B)  $5,782.85 
C)  $6,087.21 
D)  $6,407.59 
E)  $6,744.83

Question 18

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

Accepted Answer

A) True 
 B)False

Question 19

You have purchased a U.S. Treasury bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate will you earn on this bond?

Accepted Answer

A)  3.82% 
B)  4.25% 
C)  4.72% 
D)  5.24% 
E)  5.77%

Question 20

Cochrane Associate's net sales last year were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?

Accepted Answer

A)  $845.03 
B)  $889.51 
C)  $936.33 
D)  $983.14 
E)  $1,032.30

Exam 28: Time Value of Money

On January 1, 2016, your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2016?

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?

Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan.

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?

Your investment account pays 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.

Which of the following statements is CORRECT?

If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

Which of the following statements is CORRECT?

Your aunt wants to retire and has $375,000. She expects to live for another 25 years and to earn 7.5% on her invested funds. How much could she withdraw at the end of each of the next 25 years and end up with zero in the account?

Geraldine was injured in a car accident, and the insurance company has offered her the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave her as well off financially as with the annuity?

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

You have purchased a U.S. Treasury bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate will you earn on this bond?

Cochrane Associate's net sales last year were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?