Question

A sum of money, invested at compound interest, amounts to Rs. 16,500 in 1 year and to Rs. 19,965 in 3 years.

Find the rate per cent and the original sum of money invested.

Answer 1

Amount(1) = 16500
Amount(3)= 19965.
Formula-
Amount(1) = $P(1+\frac{r}{100}{)}^n$
n= no. of years
16500=$P(1+\frac{r}{100}{)}^1$

19965=$P(1+\frac{r}{100}{)}^3$

On dividing them we have
$\frac{19965}{16500}=\frac{P(1+\frac{r}{100}{)}^3}{P(1+\frac{r}{100}{)}^1}$
[P gets cancelled]

$\frac{19965}{16500}=(1+\frac{r}{100}{)}^2$

$\frac{121}{100}=(1+\frac{r}{100}{)}^2$

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

$\frac{11-10}{10}=\frac{r}{100}$

$\frac{1}{10}\times 100=r$

R= 10%

Therefore, original sum = 15000