# A certain sum of money amounts to rupees 7260 in 2 years and to rupees 7986 in 3 years, interest is compounded annually. Find the rate of interest in percent per annum.

Given :

The money amounts to Rupees 7260 in 2 years and Rupees 7986 in 3 years and the interest is being compounded annually.

To do :

We have to find the rate of interest.

Solution :

Let the principal amount be P and the rate of interest be r.

Therefore,

$P(1+\frac{r}{100})^2 = 7260$...................(i)

$P(1+\frac{r}{100})^3 = 7986$.................(ii)

Dividing (ii) by (i),

$\frac{P(1+\frac{r}{100})^3}{P(1+\frac{r}{100})^2} = \frac{7986}{7260}$

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

$\frac{r}{100} = 1.1-1$

$r = 0.1 \times 100$

$r = 10$

Therefore, the rate of interest is 10%.

$P\left( 1+\frac{r}{100}\right)^{2} =7$The rate percent per annum is 10%.

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Updated on: 10-Oct-2022

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