Question

The difference between the simple interest and compound interest for a certain sum of money for 3 years at $5\%$ p.a. is $Rs61.$ Find the sum .

Answer 1

Given Rate of interest is $r=5\%=0.05$

Let sum be $P$

Time is $t=3$ years

Interest is compounded yearly once $⟹n=1$

Amount $=P(1+\frac{r}{n}{)}^{nt}=P\times (1+0.05{)}^3=1.158P$

Interest is $A-P=0.158P$

Simple Interest is $\frac{P\times 5\times 3}{100}=0.15P$

Difference between simple interest and compound interest is $0.158P-0.15P=0.008P=61⟹P=7625$