Question

Ricky Fowler borrowed $70,000 on March 1, 2015. This amount plus accrued interest at 6% compounded semiannually is to be repaid March 1, 2025. To retire this debt, Ricky plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2020, and for the next 4 years. The fund is expected to earn 5% per annum. Instructions How much must be contributed each year by Ricky Fowler to provide a fund sufficient to retire the debt on March 1, 2025?

Short answer

The amount which is to be contributed annually will be $29,202.

Step-by-step solution

Calculation of future cash flow

$$\begin{gathered} \mathbf{Future}\mathbf{}\mathbf{Value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{cashflow}\mathbf{=}\mathbf{Amount}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{Factor} \\ \mathbf{=}\mathbf{70}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{80611} \\ \mathbf{=}\mathbf{\$}\mathbf{126}\mathbf{,}\mathbf{427}\mathbf{.}\mathbf{70} \end{gathered}$$

Calculation of amount to be contributed annually

$$\begin{gathered} \mathbf{Amount}\mathbf{}\mathbf{to}\mathbf{}\mathbf{be}\mathbf{}\mathbf{contributed}\mathbf{}\mathbf{annually}\mathbf{=}\frac{\mathbf{FV}\mathbf{}\mathbf{of}\mathbf{}\mathbf{cashflow}}{\mathbf{Pv}\mathbf{}\mathbf{Factor}\mathbf{}\mathbf{of}\mathbf{}\mathbf{annuity}} \\ \mathbf{=}\frac{\mathbf{126}\mathbf{,}\mathbf{427}\mathbf{.}\mathbf{70}}{\mathbf{4}\mathbf{.}\mathbf{32948}} \\ \mathbf{=}\mathbf{\$}\mathbf{29}\mathbf{,}\mathbf{202} \end{gathered}$$