Question

A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 8 years. Find in how many years will the money become twenty-seven times of itself at the same rate of interest p.a.

Answer 1

Let the sum of money be Rs P and the rate of interest be r % p.a.

Amount at the end of 8 years = Rs 3P

Formula for amount ,$A=P(1+\frac{r}{100}{)}^n$

where n = time,p = principal and r = rate

$3P=P(1+\frac{r}{100}{)}^{8}3=(1+\frac{r}{100}{)}^8-----\left(1\right)$

Let the money becomes 27 times in n years

$27P=P(1+\frac{r}{100}{)}^{n}27=1+\frac{r}{100}{)}^n(3{)}^3=(1+\frac{r}{100}{)}^n(1+\frac{r}{100}{)}^8{)}^3=(1+\frac{r}{100}{)}^{n}from(1\left)\right(1+\frac{r}{100}{)}^{24}=(1+\frac{r}{100}{)}^n$

Comparing bases we get n = 24 years