Question

The difference between S.I. and C.I. compounded yearly at the rate of $4\%$ in two years period on a certain amount of money is Rs.$1$. Find the amount.

• A. Rs. $600$
• B. Rs. $625$
• C. Rs. $650$
• D. Rs. $675$

Answer 1

The correct option is B Rs. $625$

Let the Principal amount be P.

We know Simple Interest (S.I)= $\frac{P\times R\times T}{100}$

Where P = P , R = 4 $\%$ and T = 2

$\Rightarrow$ S.I = $\frac{P\times 4\times 2}{100}$

$\Rightarrow \frac{8P}{100}$

Compound Interest (C.I )= $P(1+\frac{r}{100}{)}^n$

where R = Rate $\%$ per term

n = no of times interest is compounded .

$\Rightarrow C.I=P[1+\frac{4}{100}{]}^2$

$\Rightarrow P\times \frac{104}{100}\times \frac{104}{100}$

$\Rightarrow P\times (1.04{)}^2$

$\Rightarrow 1.0816$

Now subtracting S.I and C.I

$S.I-C.I=1$

$\Rightarrow \frac{8}{100}P-1.0816P=1$

Since the C.I is higher than S.I

$\Rightarrow C.I-S.I=1$

$\Rightarrow C.I-S.I=(1.0816-0.008)P$

$\Rightarrow 1.006P=1$

$\Rightarrow 1.0016=\frac{1}{P}$

$\Rightarrow P=\frac{0.1}{1.0016}$

$\Rightarrow P=625$

The principal Amount is Rs $625$.