Question

Using the appropriate interest table, compute the present values of the following periodic amounts due at the end of the designated periods. (a) \(30,000 receivable at the end of each period for 8 periods compounded at 12%. (b) \)30,000 payments to be made at the end of each period for 16 periods at 9%. (c) $30,000 payable at the end of the seventh, eighth, ninth, and tenth periods at 12%

Short answer

The present value of when the amount is receivable at the end of each period for 8 periods compounded at 12% will be $149029.20, at the end of each period for 16 periods at 9% will be $249,376.80 and present value payable at the end of seventh, eighth, ninth, and tenth periods will be $46,164.

Step-by-step solution

Computation of present value when the amount is receivable at the end of each period for 8 periods.

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}& =& \mathrm{Receivables}\times \mathrm{PV}\mathrm{annuity}\mathrm{factor}\\ & =& 30,000\times 4.88965\\ & =& \$149,029.20\end{array}$

Calculation of Present Value of the payment made at the end of each period

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}& =& \mathrm{Receivables}\times \mathrm{PV}\mathrm{annuity}\mathrm{factor}\\ & =& 30,000\times 8.31256\\ & =& \$249,376.80\end{array}$

Computation of present value payable at the end of seventh, eighth, ninth, and tenth periods.

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}& =& \mathrm{Receivables}\times \mathrm{PV}\mathrm{annuity}\mathrm{factor}\\ & =& 30,000\times (0.45234+0.40388+0.36061+0.32197)\\ & =& \$46,164\end{array}$