Question

Ms. Reema Rao deposited $Rs9000$ at the end of each year in a bank. After $3years$, The amount accumulated was $Rs29790$. Find the annual rate of compounding.

Answer 1

According to the question,

Ms.Reema Rao will get $2years$ interest for first deposited $Rs,9000$

$1year$ interest for second deposited $Rs,9000$ and

no interest for third deposited $Rs,9000$

Let , the rate of interest be $R$% p.a then,

$9000{(1+\frac{R}{100})}^2+9000(1+\frac{R}{100})+9000=29790$

$⟹9000{(1+\frac{R}{100})}^2+9000(1+\frac{R}{100})=20790$

Let, $1+\frac{R}{100}=x$ then

$9000(x^2+x)=20790$

$⟹x^2+x=\frac{20790}{9000}=\frac{231}{100}$

$⟹100x^2+100x-231=0$

$⟹(10x-11)(10x+21)=0$

$⟹x=\frac{11}{10}$ (Since x can't be -ve)

$⟹1+\frac{R}{100}=\frac{11}{10}$

$⟹R=10$

i.e., Rate of interest $=10$ %