Question 1

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

Accepted Answer

A)  The periodic rate of interest is 1.5% and the effective rate of interest is 3%. 
B)  The periodic rate of interest is 6% and the effective rate of interest is greater than 6%. 
C)  The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%. 
D)  The periodic rate of interest is 3% and the effective rate of interest is 6%. 
E)  The periodic rate of interest is 6% and the effective rate of interest is also 6%.

Question 2

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 3

You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?

Accepted Answer

A)  $1,994.49 
B)  $2,099.46 
C)  $2,209.96 
D)  $2,326.27 
E)  $2,442.59

Question 4

You have a chance to buy an annuity that pays $2,500 at the end of each year for 3 years. 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 5

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

Accepted Answer

A) True 
 B)False

Question 6

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 smaller the present value of a given lump sum to be received at some future date.

Accepted Answer

A) True 
 B)False

Question 7

Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Accepted Answer

A)  The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. 
B)  Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant. 
C)  Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant. 
D)  The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year. 
E)  The outstanding balance declines at a slower rate in the later years of the loan's life.

Question 8

Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?

Accepted Answer

A)  7.48 
B)  8.80 
C)  10.35 
D)  12.18 
E)  14.33

Question 9

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

Accepted Answer

A) True 
 B)False

Question 10

If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.

Accepted Answer

A) True 
 B)False

Question 11

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%?

Accepted Answer

A)  18.58% 
B)  19.56% 
C)  20.54% 
D)  21.57% 
E)  22.65%

Question 12

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?

Accepted Answer

A)  39.60 
B)  44.00 
C)  48.40 
D)  53.24 
E)  58.57

Question 13

You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

Accepted Answer

A)  $18,369 
B)  $19,287 
C)  $20,251 
D)  $21,264 
E)  $22,327

Question 14

A time line is not meaningful unless all cash flows occur annually.

Accepted Answer

A) True 
 B)False

Question 15

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

Accepted Answer

A)  $3,704.02 
B)  $3,889.23 
C)  $4,083.69 
D)  $4,287.87 
E)  $4,502.26

Question 16

Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.

Accepted Answer

A)  Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments). 
B)  Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments). 
C)  Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). 
D)  Investment D pays $2,500 at the end of 10 years (just one payment). 
E)  Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).

Question 17

Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?

Accepted Answer

A)  $1,063,968 
B)  $1,119,966 
C)  $1,178,912 
D)  $1,240,960 
E)  $1,303,008

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

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. By how much would you reduce the amount you owe in the first year?

Accepted Answer

A)  $2,404.91 
B)  $2,531.49 
C)  $2,658.06 
D)  $2,790.96 
E)  $2,930.51

Exam 5: Time Value of Money

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

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

You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?

You have a chance to buy an annuity that pays $2,500 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

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 smaller the present value of a given lump sum to be received at some future date.

Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%?

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?

You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

A time line is not meaningful unless all cash flows occur annually.

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.

Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?

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

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. By how much would you reduce the amount you owe in the first year?