In how many years will Rs 6250 amount to Rs 7290 at 8% per annum, compounded annually?
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
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