Question

The difference between the simple interest on a certain sum at the rate off $10\%$ per annum for $2$ years and compound interest which is compounded every $6$ months is Rs. $12000$. What is the principal sum?

• A. $756331.49$
• B. $753881.25$
• C. $60000.20$
• D. $773881.49$

Answer 1

Answer: (D)

$773881.49$

Let the sum be $P$.

Compound interest $=$ Amount $-$ Principal
$=P{(1+\frac{R/2}{100})}^{2\times 2}-P$
$=P{(1+\frac{10/2}{100})}^4-P$
$=P{(1+\frac{1}{20})}^4-P$

$=P{\left(\frac{21}{20}\right)}^4-P$
Simple interest on $P$ at $10\%$ for $2$ years $=$ $\frac{PRT}{100}$
We know, SI $=$ $\frac{P\times 10\times 2}{100}=\frac{P}{5}$
Given that difference between compound interest and simple interest $=12000$
$P{\left(\frac{21}{20}\right)}^4-P-\frac{P}{5}=12000$
$P[{\left(\frac{21}{20}\right)}^4-1-\frac{1}{5}]=12000$
$P\left[\frac{194481-160000-32000}{160000}\right]=12000$
$P\left[\frac{2481}{160000}\right]=12000$
$P=$ Rs. $773881.49$