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# Multiple Choice questions on Time Value of Money

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Identify the letter of the choice that best completes the statement or answers the question.

____ 1. How much must be invested today to have \$1,000 in two years if the interest rate is 5%?
a. \$909.09
b. \$900.00
c. \$907.00
d. \$950.00

____ 2. Find the present value of \$100 to be received at the end of two years if the discount rate is 12% compounded monthly.
a. \$66.50
b. \$78.76
c. \$68.80
d. \$91.80
e. \$79.75

____ 3. What is the most you should pay to receive the following cash flows if you require a return of 12 percent?

Year 1 \$5,000
Year 2 \$8,000
Year 3 \$12,000
Year 4-10 \$15,000

a. \$58,580
b. \$104,135
c. \$68,105
d. none of the above

____ 4. Find the future value in two years of \$100 that is deposited in an account, which pays 12%, compounded monthly.
a. \$160.00
b. \$112.70
c. \$118.80
d. \$125.40
e. \$126.97

____ 5. You have borrowed \$180,000 to buy a new home. You plan to make monthly payments over a 25-year period. The bank has offered you a 10% interest rate compounded monthly. Calculate the total amount of interest you will pay the bank over the life of the loan.
a. \$301,499
b. \$307,541
c. \$310,545
d. \$319,766

____ 6. You have borrowed \$130,000 to buy a new motor home. Your loan is to be repaid over 15 years at 8% compounded monthly If you pay an extra \$200 per month on the motor home, how many years will it take to pay off the loan?
a. 10.3 years
b. 11. 5 years
c. 12.8 years
d. 13.3 years

____ 7. A perpetuity has a cash flow of \$20 and a discount rate of 10%. What is the value of the perpetuity?
a. \$22
b. \$500
c. \$200
d. none of the above

____ 8. Keith Stone has a 10-year-old daughter, Kate, who will be entering college in 8 years. Keith estimates college costs to be \$16,000, \$17,000, \$18,000 and \$19,000 payable at the beginning of each of Kate's four years in college. How much must Keith save each year (assume end of year payments) for each of the next 8 years to have enough savings to pay for Kate's education when she starts college? Assume Keith can earn 9% on his savings.
a. \$5,569
b. \$7,720
c. \$5,108
d. \$7,677

____ 9. Calculate the amount to be received at the end of year 1 that is equivalent to \$150 at the end of year 1, \$450 at the end of year 2, and \$300 at the end of year 3, given a discount rate of 10%.
a. \$807
b. \$817
c. \$887
d. \$975
e. \$1,331

____ 10. You are considering an investment that will pay you \$100 in Year 1, \$500 in Year 2, \$0 in Year 3 and \$600 in Year 4. If you require a 12% return, what is the most you should pay for this investment today? (Round to nearest \$)
a. \$915
b. \$869
c. \$734
d. \$698

#### Solution Preview

Note: the abbreviations have the following meanings

PVIF= Present Value Interest Factor
PVIFA= Present Value Interest Factor for an Annuity
FVIF= Future Value Interest Factor
FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations
PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
PVIF( n, r%)= =1/(1+r%)^n
FVIF( n, r%)= =(1+r%)^n
FVIFA( n, r%)= =[(1+r%)^n -1]/r%

^ stands for raised to the power of

Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

c. 1 How much must be invested today to have \$1,000 in two years if the interest rate is 5%?
a. \$909.09
b. \$900.00
c. \$907.00
d. \$950.00

Frequency= A Annual
No of years= 2
No of Periods= 2
Discount rate annually= 5.00% annual
Discount rate per period= 5.0000% Annual
n= 2
r= 5.00%
PVIF (2 periods, 5.% rate ) = 0.907029

Future value= 1,000
Therefore, present value= 907.03 =1000x0.907029

b. 2 Find the present value of \$100 to be received at the end of two years if the discount rate is 12% compounded monthly.
a. \$66.50
b. \$78.76
c. \$68.80
d. \$91.80
e. \$79.75

Frequency= m Monthly
No of years= 2
No of Periods= 24
Discount rate annually= 12.00% annual
Discount rate per period= 1.0000% Monthly
n= 24
r= 1.00%
PVIF (24 periods, 1.% rate ) = 0.787566

Future value= 100
Therefore, present value= 78.76 =100x0.787566

c.
____ 3 What is the most you should pay to receive the following cash flows if you require a return of 12 percent?

Year 1 \$5,000
Year 2 \$8,000
Year 3 \$12,000
Year 4-10 \$15,000

a. \$58,580
b. \$104,135
c. \$68,105
d. none of the above