Question

A sum of money amounts to $Rs.11910.16$ in $1\frac{1}{2}$ years at $12\%$ per annum interest being compounded semi annually. Find the sum.

Answer 1

Let the total amount be A=Rs.$11910.16$ and sum be Rs. P
Rate of interest R=$12\%$
Time, t=$1\frac{1}{2}$ years for semi-annually or 3 years for R=$\frac{12}{2}=6\%$
As we know that A=P$(1+\frac{R}{100}{)}^3$
$\Rightarrow 11910.16=P(1+\frac{6}{100}{)}^3$
$\Rightarrow 11910.16=P(1+\frac{3}{50}{)}^3$
$\Rightarrow 11910.16=P(\frac{53}{50}{)}^3$
$\Rightarrow P=11910.16(\frac{50}{53}{)}^3$
$\therefore P=Rs.10,000$