Question

Find the present value of an ordinary annuity of $8$ quarterly payments of Rs. $500$ each, the rate of interest being $8\%$ p.a. compounded quarterly.

• A. Rs. $3660.20$
• B. Rs. $3662.50$
• C. Rs. $4275$
• D. Rs. $3660$

Answer 1

The correct option is B Rs. $3662.50$

Given, $A=$ Rs $500$, $n=8$

Also, $r=\frac{8}{100}\times \frac{1}{4}=0.02$

$\therefore V=\frac{A}{r}\times [1-(1+r{)}^{(-n)}]=\frac{500}{0.02}\times [1-(1.02{)}^{(-8)}]$

Now, let $x=(1.02{)}^{(-8)}$

$\Rightarrow \log x=-8\log 1.02=-8\left(0.0086\right)$

$\Rightarrow \log x=-0.0688$

$\Rightarrow x=0.8535$

$\Rightarrow V=\frac{500}{0.02}\times [1-0.8535]=$ Rs. $3662.50$

Thus, the present value of annuity is Rs. $3662.50$.