Question

Using the appropriate interest table, answer the following questions. (Each case is independent of the others). (a) What is the future value of 20 periodic payments of \(4,000 each made at the beginning of each period and compounded at 8%? (b) What is the present value of \)2,500 to be received at the beginning of each of 30 periods, discounted at 5% compound interest? (c) What is the future value of 15 deposits of \(2,000 each made at the beginning of each period and compounded at 10%? (Future value as of the end of the fifteenth period.) (d) What is the present value of six receipts of \)1,000 each received at the beginning of each period, discounted at 9% compounded interest?

Short answer

The future value of $4,000 will be $183,047.6, the present value of $2,500 received will be $40352.68, the future value of$2,000 deposits will be $63,544.96 and the present value of $1,000 received will be $4889.65.

Step-by-step solution

Computation of future value

$\begin{array}{rcl}\mathrm{FV}& =& \mathrm{Payment}\times \mathrm{FV}\mathrm{of}\mathrm{annuity}\\ & =& 4,000\times 45.7619\\ & =& \$183,047.6\end{array}$

Computation of present value

$\begin{array}{rcl}\mathrm{PV}& =& \mathrm{Payment}\mathrm{received}\times \mathrm{PV}\mathrm{of}\mathrm{annuity}\mathrm{due}\\ & =& 2,500\times 16.4107\\ & =& \$40,352\end{array}$

Computation of future value

$\begin{array}{rcl}\mathrm{FV}& =& \mathrm{Deposits}\times \mathrm{FV}\mathrm{of}\mathrm{annuity}\\ & =& 2,000\times 31.77248\\ & =& \$63,544.96\end{array}$

Computation of present value

$\begin{array}{rcl}\mathrm{PV}& =& \mathrm{Receipts}\times \mathrm{PV}\mathrm{of}\mathrm{annuity}\mathrm{due}\\ & =& 1,000\times 4.88965\\ & =& \$4,889.65\end{array}$