Question

A sum of money amounts to $Rs.11910.16$ in $1.5$ years at $12\%$ per annum interest being compounded semi annually. Find the sum.

Answer 1

Given:

Total amount $\left(A\right)=Rs.11910.16$.

Rate of Interest $\left(R\right)=12\%$ per annum.

$\Rightarrow$ Rate of Interest $\left(R\right)=\frac{12}{2}\%=6\%$ per semi annum

Time $\left(T\right)=1.5$ years.

$\Rightarrow n=3$ half years

Now, $A=P(1+\frac{R}{100}{)}^n$

$\Rightarrow 11910.16=P(1+\frac{6}{100}{)}^3$

$\Rightarrow 11910.16=P(1+\frac{3}{50}{)}^3$

$\Rightarrow 11910.16=P(\frac{53}{50}{)}^3$

$\Rightarrow 11910.16=P\times \frac{53}{50}\times \frac{53}{50}\times \frac{53}{50}$

$\Rightarrow 11910.16\times \frac{50}{53}\times \frac{50}{53}\times \frac{50}{53}=P$

$\Rightarrow \frac{1191016}{100}\times \frac{125000}{148877}=P$

$\Rightarrow \frac{8}{1}\times \frac{12500}{1}=P$

$\Rightarrow 100000=P$
Therefore, the sum is $Rs.100000$.