Question

A certain sum invested at $4\%$ p.a. compounded semi-annually amounts to Rs. $78,030$ at the end of one year. Find the sum invested at the beginning of year $1$.

• A. Rs. $70,000$
• B. Rs. $65,000$
• C. Rs. $75,000$
• D. Rs. $85,000$

Answer 1

The correct option is C Rs. $75,000$

$A_n=78,030$
$n=2\times 1=2$
$i=4\times 1/2\%=2\%=0.02$
$P(inRs.)=?$
We have $A_n=P(1+i{)}^n$
$A_2=P(1+0.02{)}^2$
$78,030=P(1.02{)}^2$

$P=\frac{78,030}{{1.02}^2}$

$P=75,000$ Thus the sum invested is Rs. $75,000$ at the beginning of $1$ year.