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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%.
The rate percent per annum is 10%.
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