Question

Find the amount and the compound interest when the interest is compounded annually.
(i) Principal $=Rs.4000$ , Time $=2$ years, Rate = $10\%$ per annum.
(ii) Principal $=Rs.4000$ , Time $=2$ years, Rate $=15\frac{1}{2}\%$ per annum.

Answer 1

Given:

Principal $P=Rs.4000$

Time $T=2$ years

Rate of interest $R=10\%$ per annum.

So, $n=2$

Total amount on compounded annually,

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

$A=4000\times (1+\frac{10}{100}{)}^2$

$A=4000\times (1+\frac{1}{10}{)}^2$

$A=4000\times (\frac{11}{10}{)}^2$

$A=4000\times \frac{11}{10}\times \frac{11}{10}$

$A=40\times 121$

$A=4840$

Therefore, the total amount $=Rs.4840$

The compound interest formula is given by

$C.I=A-P$

$\Rightarrow C.I=Rs.4840-Rs.4000$

$\Rightarrow C.I=Rs.840$

(ii)

Given,

Principal $\left(P\right)=Rs.4000$

Time $\left(T\right)=2$ years

Rate of interest $\left(R\right)=15\frac{1}{2}\%=\frac{31}{2}\%$ per annum

$n=2$

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

$\Rightarrow A=4000(1+\frac{31}{2\times 100}{)}^2$

$\Rightarrow A=4000(1+\frac{31}{200}{)}^2$

$\Rightarrow A=4000(\frac{231}{200}{)}^2$

$\Rightarrow A=4000\times \frac{231}{200}\times \frac{231}{200}$

$\Rightarrow A=\frac{231}{1}\times \frac{231}{10}$

$\Rightarrow A=Rs.5336.10$

Therefore, the total amount $A=Rs.5336.10$

The compound interest formula is given by

$C.I=A-P$

$\Rightarrow C.I=Rs.5336.10-Rs.4000$

$\Rightarrow C.I=Rs.1336.1$