If Rs 9000 amounts to Rs 11902 in two years, compounded annually find the rate of interest per annum

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By using the formula, find the amount and compound interest on:Rs 9000 for 2 years 4 months at 10 % per annum compounded annually.

Solution

Given: Principal $\left(P\right)=Rs.9000$

Rate $\left(R\right)=10\%$ per annum

Time $\left(n\right)=2$ years $4$ months

$=2\frac{1}{3}$ years [$\because 1$ year $=12$ months]

Amount for $2$ years

$\therefore$ Amount $\left(A\right)=P{(1+\frac{R}{100})}^n$

$=Rs.9000{(1+\frac{10}{100})}^2$

$=Rs.9000\times \frac{11}{10}\times \frac{11}{10}$

$=Rs.10890$

For the next $\frac{1}{3}$ years, Principal $=$ Amount for $2$ years $=Rs.10890.$

Interest for $\frac{1}{3}$ years $=\frac{P\times R\times n}{100}$

$=\left(\frac{10890\times 10\times \frac{1}{3}}{100}\right)$

$=Rs.363$

So, the total Amount for $2\frac{1}{3}$ years $=Rs.10890+363=Rs.11253$

$\therefore C.I.=A-P=Rs.11253-Rs.9000$

$=Rs.2253$

Mathematics

Secondary School Mathematics VIII

Standard VIII