The Time Value of Money
Complete the following problems. You will likely use a spreadsheet for this assignment but you may choose to type up your answers in a Word document. In either case, be sure to show your work.
Problem 1: Compound Interest
To what amount will the following SAR investments accumulate?
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A)
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Investment
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7,000
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Years
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8
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Percent
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9%
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FV =
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B)
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Investment
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11,000
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Years
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10
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Percent
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7%
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FV =
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C)
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Investment
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20,000
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Years
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6
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Percent
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8%
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FV =
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D)
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Investment
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750
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Years
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12
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Percent
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12%
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FV =
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Problem 2: Present Value
What is the present value of the following future amounts?
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A)
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FV
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1,200
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Years
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7
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Percent
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11%
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PV =
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B)
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FV
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400
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Years
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6
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Percent
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6%
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PV =
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C)
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FV
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1,500
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Years
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8
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Percent
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4%
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PV =
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D)
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FV
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2,500
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Years
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8
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Percent
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20%
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PV =
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Problem 3: Future Value
Sales of a new finance book were 20,000 copies this year and were expected to increase by 15 percent per year. What are expected sales during each of the next 3 years?
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DATA
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Copies
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20,000
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Percent
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15%
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Years
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3
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Solution:-
FV for 1st yr =
FV for 2nd yr =
FV for 3rd yr =
Problem 4: Present-Value Comparison
Assuming you can earn 9 percent on your money, which of the following offers should you choose? SAR 1200 today; SAR 12,500 in 11 years; or SAR 30,000 in 25 years?
Solution:-
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Percent
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9%
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Years
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Amount
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PV
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A
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Today
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1,200
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B
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12
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12,500
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C
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25
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30,000
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Which offer should you choose and why?
Problem 5: Compound Annuity
What is the accumulated sum of each of the following streams of payments?
a. SAR 1,500 a year for 8 years compounded annually at 6 percent
b. SAR 1,000 a year for 6 years compounded annually at 12 percent
c. SAR 350 a year for 5 years compounded annually at 5 percent
d. SAR 125 a year for 4 years compounded annually at 4 percent
Solution:-
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A)
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Pymt
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1,500
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Years
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8
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Percent
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6%
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FV =
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B)
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Pymt
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1,000
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Years
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6
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Percent
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12%
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FV =
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C)
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Pymt
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350
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Years
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5
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Percent
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5%
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FV =
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D)
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Pymt
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125
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Years
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4
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Percent
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4%
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FV =
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Problem 6: Compound Interest with Nonannual Periods
a. Calculate the future sum of SAR 7,000, given that the money will be held in the bank for 5 years at an annual interest rate of 6 percent.
b. Recalculate part a. assuming the interest rate is (1) an APR of 6 percent compounded semiannually and (2) an APR of 6 percent compounded bimonthly.
c. Recalculate parts a. and b. for an APR of 12 percent
d. Recalculate part a. using a time horizon of 12 years (the APR is still 6 percent).
e. With respect to the effect of changes in the stated interest rate and holding periods on future sums in parts c. and d., what conclusions do you draw when you compare these figures with the answers found in parts a. and b.?
Solution
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A)
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PV
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7,500
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Years
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5
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Percent
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6%
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FV =
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B)
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Semiannual
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2
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Bimonthly
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6
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C)
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Rate
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12%
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Annual
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Semiannual
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Bimonthly
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D)
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Years
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12
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Annual
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