Question

In how many years will Rs. 6,250 amounts to Rs. 6,760 at 4% per anum compound interest?

Answer 1

Given P = Rs. 6,250, A = Rs. 6,760, R = 4%, We have to find n. We know,
$A=P{(1+\frac{R}{100})}^n$.
Thus
$6,760=6,250{(1+\frac{4}{100})}^n\Rightarrow {(1+\frac{4}{100})}^n=\frac{6,760}{6,250}$
$\Rightarrow {(1+\frac{4}{100})}^n={\left(\frac{26}{25}\right)}^2$
$=\Rightarrow {\left(\frac{26}{25}\right)}^n={\left(\frac{26}{25}\right)}^2\Rightarrow n=2$,
since when bases are the same on the both sides, the powers are equal.
Hence, Rs. 6,250 will amount to Rs. 6,760 in 2 years.