Question

A certain sum of money, placed out at compound interest, amounts to Rs.6,272 in 2 years and to Rs. 7,024.64 in 3 years. Find the rate of interest and the sum of money.

Answer 1

$WeknowthatCompoundInterest=Amount-Principal$

$Amountfor3rdyear-Amountfor2ndyearwillbetheinterestfor3rdyear$

$Amountfor2ndyearwillserveasPrincipalfor3rdyear$

$Asperproblem7024.64-6272=752.64\left(compoundinterest\right)$

$\Rightarrow P{(1+\frac{r}{100})}^3-P{(1+\frac{r}{100})}^2=752.64$

$\Rightarrow P{(1+\frac{r}{100})}^2[(1+\frac{r}{100})-1]=752.64$

$\Rightarrow 6272\left[\frac{r}{100}\right]=752.64$

$\Rightarrow 6272r=75264$

$r=\frac{75264}{6272}=12$

Let the sum be P

AS PER PROBLEM, $6272=P{(1+\frac{12}{100})}^2$

$6272=P1.2544$

$P=\frac{6272}{1.2544}=5000$

Sum of money is 5000 and rate of interest is 12 percent.