Find the compound interest at the rate of $10 %$ per annum for four years on the principal which in four years at the rate of $4 %$ per annum gives $R s . 1600$ as simple interest.

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Solution

Let $P$ be the principal.

This principal gives $R s . 1600$ as $S . I .$ in four years at the rate of $4 %$ per annum.
$S . I = \frac{P \times R \times T}{100}$

$\Rightarrow P = \frac{S . I \times 100}{R \times T}$

$\Rightarrow P = \frac{R s . 1600 \times 100}{4 \times 4}$
$\Rightarrow P = R s . 10000$

Now, we have

$P = R s . 10000, R = 10 %$ and $n = 4$

$∴$ Amount after $4$ years
$A = P {(1 + \frac{R}{100})}^{n}$

$= R s . 10000 \times {(1 + \frac{10}{100})}^{4}$

$= R s . 10000 \times {(1 + \frac{1}{10})}^{4}$

$= R s . 10000 \times {(\frac{11}{10})}^{4}$

$= R s . 10000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10}$
$= R s . 14641$

$∴$ Compound interest $C . I = A - P$
$= R s . 14641 - R s . 10000$
$= R s . 4641$

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Find the compound interest at the rate of 10% per annum for four years on the principal which in four years at the rate of 4% per annum gives Rs. 1600as simple interest.

Find the compound interest at the rate of $10 %$ per annum for four years on the principal which in four years at the rate of $4 %$ per annum gives $R s . 1600$ as simple interest.