Question

At what rate per cent will a sum of Rs. 4,000 yield Rs. 1,324 as compound interest in 3 years?

Answer 1

Given that principal = Rs.4000

And C I = Rs.1324

Amount = Principal + C.I

A = 4000 + 1324 .

A = Rs. 5324

let the rate of interest = r%.

Given time = 3 years

Amount= P$(1+\frac{R}{100}{)}^n$

⇒ 5324 = 4000$(1+\frac{r}{100}{)}^3$​​​​​​​

⇒ $\frac{5324}{4000}$ = $(1+\frac{r}{100}{)}^3$​​​​​​​​​​​​​​​​​​​​​

⇒ $\frac{1331}{1000}$ = $(1+\frac{r}{100}{)}^3$​​​​​​​​​​​​​​​​​​​​​​​​​​​​

⇒ $\frac{{11}^3}{{10}^3}$ = $(1+\frac{r}{100}{)}^3$​​​​​​​​​​​​​​​​​​​​​ [ cube root on both sides]

⇒ $\frac{11}{10}$ = $(1+\frac{r}{100})$​​​​​​​​​​​​​​​​​​​​​

⇒ $\frac{11}{10}$ - 1 = $\frac{r}{100}$​​​​​​​​​​​​​​​​​​​​​

⇒ $\frac{1}{10}$ = $\frac{r}{100}$

∴ r =10%

Hence the rate of interest is 10%.