By using the formula, find the amount and compound interest on:

Question:

By using the formula, find the amount and compound interest on:

Rs 10240 for 3 years at $12 \frac{1}{2} \%$ per annum compounded annually.

Solution:

Principal amount, $P=$ Rs 62500

Rate of interest, $R=12 \%$ p. a.

Time, $n=2$ years 6 months $=\frac{5}{2}=2 \frac{1}{2}$ years

The formula for the amount including the compound interest is given below :

$A=$ Rs. $P\left(1+\frac{R}{100}\right)^{\mathrm{n}}$

$\Rightarrow A=$ Rs. $62500\left(1+\frac{12}{100}\right)^{2} \times\left(1+\frac{\frac{1}{2} \times 12}{100}\right)$

$\Rightarrow A=$ Rs. $62500\left(1+\frac{12}{100}\right)^{2} \times\left(1+\frac{6}{100}\right)$

$\Rightarrow A=$ Rs. $62500 \times 1.12 \times 1.12 \times 1.06$

$\Rightarrow A=$ Rs. 83104

i.e., the amount including the compound interest is Rs $83104 .$

$\therefore$ Compound interest $=$ Rs. $(83104-62500)=$ Rs. 20604

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