Question

The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is ₹1. The value of principal amount is _____.

• A. ₹625
• B. ₹650
• C. ₹725
• D. ₹750

Answer 1

The correct option is A

₹625

Let the sum be $₹x.$

Amount after 2 years on $₹x$ at 4% per annum when interest is compounded annually

$=x(1+\frac{4}{100}{)}^2=x(\frac{104}{100}{)}^2$

Compound Interest $=x(\frac{104}{100}{)}^2-x$

$=x\left[\right(\frac{104}{100}{)}^2-1]=x[(\frac{26}{25}{)}^2-1]=x[\frac{676}{625}-1]=x\left[\frac{51}{625}\right]=\frac{51x}{625}$

Simple Interest =$\frac{PRT}{100}=\frac{x\times 4\times 2}{100}=\frac{2x}{25}$

Given that difference between compound interest and simple interest is ₹1.

$\Rightarrow \frac{51x}{625}-\frac{2x}{25}=1$

$\Rightarrow \frac{51x-50x}{625}=1$

$\Rightarrow x=625$

$\therefore$ the principal amount is ₹625.