Question

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

• A. $4375$
• B. $4275$
• C. $4175$
• D. $4475$

Answer 1

The correct option is B $4275$

$\Rightarrow$ Here, $A=Rs.500,n=8$ and $r=\frac{8}{100}\times \frac{1}{4}=0.02$

$\Rightarrow$ $V=\frac{A}{r}\times [1-(1+r{)}^{-n}]$

$\Rightarrow$ $V=\frac{500}{0.02}\times [1-(1.02{)}^{-8}]$

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

$\Rightarrow$ $logx=-8log1.02=-8\left(0.0086\right)$

$\Rightarrow$ $logx=-0.0688$

$\Rightarrow$ $x=0.8535$

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

$\Rightarrow$ Now, $M=\frac{A}{r}\times \left[\right(1+r{)}^n-1]$

$\Rightarrow$ $\frac{500}{0.02}\times \left[\right(1.02{)}^8-1]$

$\Rightarrow$ Let $x=(1.02{)}^8$

$\Rightarrow$ $logx=8log\left(1.02\right)=0.0688$

$\Rightarrow$ $x=1.171$

$\therefore$ $M=\frac{500}{0.02}\times [1.171-1]=Rs.4275$

$\therefore$ The present value of annuity is $Rs.3662.50$ and amount is $Rs.4275$