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1)
1). What is the present value of a $520 perpetuity discounted back to the present at 4.06 percent.
The answer should be calculated to two decimal places.
2). If you want to have $447,917 in 10 years, how much money should you put in a savings account today?
Assume that savings account pays you 10.0 percent and it is compounded annually. Round the answer to two places
3). An investment will pay $114 two years from now, $924 four years from now, and $1,414 five years from now. You are going to reinvest these cash flows at a rate of 9.68 percent per year. What is the future value of this investment at the end of year five?
Round the answer to two decimal places.
4). 30 years ago, the average home sale price in your hometown was $79,478. Today the average price of a house is $345,663. What was the average annual rate of change in the price of houses over this time period? (you should calculate the compound growth rate in this problem).
Round the answer to two decimal places in percentage form. (write the percentage sign in the "units" box)
5). Large -cap stocks had the nominal rate of return of 13.32 percent. The rate inflations during the last year was 3.71 percent. What is the real rate of return for large-cap stocks?
Round the answer to two decimal places in percentage form. (write the percentage sign in the "units" box)
Expert Solution
1). Computation of the present value of perpetuity:-
Present value of perpetuity = Annual cash flows / Interest rate
= $520 / 4.06%
= $12,807.88
2). Computation of the present value:-
FV = PV*(1+Rate)^n
$447,917 = PV*(1+10%)^10
PV = $447,917 / 2.5937
= $172,691.39
3). Computation of the future value of the investment at the end of year 5:-
Future Value = (114*(1+9.68%)^3) + (924*(1+9.68%)) + 1,414
= $150.41 + $1,013.44 + $1,414
= $2,577.86
4). Computation of the average annual rate:-
FV = PV*(1+Rate)^n
$345,663 = $79,478*(1+Rate)^30
(1+Rate)^30 = $345,663 / $79,478
(1+Rate) = 4.3492^(1/30)
Rate = 1.0502 - 1
= 5.02%
5). Computation of the real rate of return:-
(1+Nominal rate of return) = (1+Inflation rate)*(1+Real rate of return)
(1+13.32%) = (1+3.71%)*(1+Real rate of return)
(1+Real rate of return) = (1+13.32%)/(1+3.71%)
Real rate of return = 1.0927 - 1
= 9.27%
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