Question

A sum of money invested for $3$ years at $5\%$ p.a. compound interest reckoned annually. If the total interest earned be $Rs2522$ then find the sum of money.

Answer 1

Let $P$ be the principal.

Rate of interest, $R=5\%$ p.a.

Time, $n=3$ yrs

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

$\Rightarrow P+CI=P(1+\frac{5}{100}{)}^3$ [$\because$ Amount, $A=P+CI$]

$\Rightarrow P+2522=P(\frac{21}{20}{)}^3$

$\Rightarrow P+2522=P\times \frac{9261}{8000}$

$\Rightarrow P(1-\frac{9261}{8000})=-2522$

$\Rightarrow P\left(\frac{1261}{8000}\right)=2522$

$\Rightarrow P=2522\times \frac{8000}{1261}=16000$

So, required sum is $Rs.16000.$