Question

Using the appropriate interest table, answer each of the following questions. (Each case is independent of the others.) (a) What is the future value of \(7,000 at the end of 5 periods at 8% compounded interest? (b) What is the present value of \)7,000 due 8 periods hence, discounted at 6%? (c) What is the future value of 15 periodic payments of \(7,000 each made at the end of each period and compounded at 10%? (d) What is the present value of \)7,000 to be received at the end of each of 20 periods, discounted at 5% compound interest?

Short answer

The future value of $7,000 compounded annually at 8% will be $10,285, the present value of $7,000 discounted at 6% will be $4,392, the future value of periodic payments of $7,000 will be $222,408, and the present value of $7,000 periodically will be $87,235.

Step-by-step solution

Step 1:Computation of future value

$$\begin{gathered} \mathbf{Future}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{factor} \\ \mathbf{=}\mathbf{7}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{4693} \\ \mathbf{=}\mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{285} \end{gathered}$$

Computation of Present value

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Future}\mathbf{}\mathbf{Value}\mathbf{\times }\mathbf{PV}\mathbf{}\mathbf{factor} \\ \mathbf{=}\mathbf{7}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{62741} \\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{392} \end{gathered}$$

Calculation of future value of the periodic payment

$$\begin{gathered} \mathbf{Future}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Periodic}\mathbf{}\mathbf{Payment}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{factor} \\ \mathbf{=}\mathbf{7}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{31}\mathbf{.}\mathbf{7725} \\ \mathbf{=}\mathbf{\$}\mathbf{222}\mathbf{,}\mathbf{408} \end{gathered}$$

Calculation of Present Value of the periodic payment

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Periodic}\mathbf{}\mathbf{Payment}\mathbf{\times }\mathbf{PV}\mathbf{}\mathbf{factor} \\ \mathbf{=}\mathbf{7}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{12}\mathbf{.}\mathbf{4622} \\ \mathbf{=}\mathbf{\$}\mathbf{87}\mathbf{,}\mathbf{235} \end{gathered}$$