In how many years will Rs 6250 amount to Rs 7290 at 8%

Solution:

Let the required time be $n$ years.

Rate of interest, $R=8 \%$

Principal amount, $P=$ Rs. 6250

Amount with compound interest, $A=$ Rs. 7290

Then, $A=P \times\left(1+\frac{R}{100}\right)^{n}$

$\Rightarrow$ A $=$ Rs. $6250 \times\left(1+\frac{8}{100}\right)^{n}$

$=$ Rs. $6250 \times\left(\frac{100+8}{100}\right)^{n}$

$=$ Rs. $6250 \times\left(\frac{100}{100}\right)^{n}$

$=$ Rs. $6250 \times\left(\frac{27}{25}\right)^{\text {n }}$

However, amount $=$ Rs. 7290

Now, Rs. $7290=$ Rs. $6250 \times\left(\frac{27}{25}\right)^{n}$

$\Rightarrow \frac{7290}{6250}=\left(\frac{27}{25}\right)^{n}$

$\Rightarrow \frac{729}{625}=\left(\frac{27}{25}\right)^{n}$

$\Rightarrow\left(\frac{27}{25}\right)^{2}=\left(\frac{27}{25}\right)^{n}$

$\Rightarrow n=2$

$\therefore$ Time, $n=2$ years