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Chapter 15: Problem 1

Suppose the interest rate is 10 percent. If \(\$ 100\) is invested at this rate today, how much will it be worth after one year? After two years? After five years? What is the value today of \(\$ 100\) paid one year from now? Paid two years from now? Paid five years from now?

Short Answer

Expert verified
After one year, the investment will be worth \$110. After two years, it will be worth \$121. After five years, it will amount to \$161.05. The present value of \$100 to be received one year from now is \$90.91, in two years it is \$82.64, and in five years it is \$62.09.

Step by step solution

01

Calculate Future Value After 1 Year

To calculate future value, use the formula \( FV = PV*(1 + r) \) where PV is the present value (initial investment), r is the interest rate in decimal. Here, PV = \$100 and r = 0.10 or 10%. Therefore, \( FV = \$100 * (1 + 0.10) = \$110 \)
02

Calculate Future Value After 2 and 5 Years

The formula for future value, when compounded annually over n years, is \( FV = PV*(1 + r)^n \). For 2 years, n=2 and for 5 years, n=5. Thus, after 2 years, \( FV = \$100*(1 + 0.10)^2 = \$121 \), and after 5 years, \( FV = \$100*(1 + 0.10)^5 = \$161.05 \)
03

Calculate Present Value 1 Year From Now

Present value can be calculated using the formula \( PV = FV/(1 + r) \). Here, FV = \$100 and the present value of \$100 paid one year from now would be \( PV = \$100/(1 + 0.10) = \$90.91 \)
04

Calculate Present Value 2 and 5 Years From Now

The present value formula for n years in the future is \( PV = FV/(1 + r)^n \). Therefore, the present value of \$100 to be received in 2 and 5 years respectively would be \( PV = \$100/(1 + 0.10)^2 = \$82.64 \) and \( PV = \$100/(1 + 0.10)^5 = \$62.09 \)

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Most popular questions from this chapter

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