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Chapter 17: Problem 71

Your perfectly reliable friend, Frank, asks for a loan and promises to pay back \(\$ 150\) two years from now. If the minimum interest rate you will accept is 8 percent, what is the maximum amount you will loan him? a) \(\$ 119\) c) \(\$ 129\) b) \(\$ 126\) d) \(\$ 139\)

Short Answer

Expert verified
a) $116 b) $124 c) $129 d) $137 Answer: c) $129

Step by step solution

01

Identify the given variables

We are given the following information: - Future value (FV) = \( \$ 150\) - Interest rate (i) = \(8 \% = 0.08\) - Time period (n) = 2 years
02

Rearrange the formula to solve for Present Value

We need to find the Present Value (PV), so we will rearrange the formula as follows: \(PV = \frac{FV}{(1+i)^n}\)
03

Plug in the given values

Now, we will plug in the values of FV, i, and n into the formula: \(PV = \frac{\$ 150}{(1+0.08)^2}\)
04

Calculate the Present Value

Calculating the expression: \(PV = \frac{\$ 150}{(1.08)^2} = \frac{\$ 150}{1.1664} \approx \$ 128.73\)
05

Choose the correct answer

The maximum amount we will loan Frank is approximately \( \$ 128.73\). Looking at the available options, the closest value is \( \$ 129\). Therefore, the correct answer is (c) \(\$ 129\).

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