Question

Calculate the present value of R1 700 received at the end of each month for 6 successive months using a discount rate of 8%

Answer 1

Present value of annuity $= annuity ×\frac{( 1 - (1/( 1+ rate)^{no\space of \space periods} )}{rate}$

Monthly Payment = 1700

Time = 6 months

Discount rate = 8%

Monthly rate = annual rate ÷12

           $= \frac{8\%}{ 12} = 0.6667\%$

Present value of annuity will be

$1700 ×\frac{( 1 - ( 1÷ (1+0.6667\%)^6) }0.6667\%\\ = 1700 × \frac{( 1 - ( 1÷(1.006667)^6) }{0.006667}\\ = 1700 ×\frac{( 1 - ( 1÷1.04067 )) }{0.006667}\\ = 1700 ×\frac{ ( 1 - 0.9609 ) }{ 0.006667}\\ = 1700 ×\frac{ ( 0.039 ) }{ 0.006667}\\ = \$9,966.17$