Tick (✓) the correct answer:
At what rate per cent per annum will a sum of Rs 7500 amount to Rs 8427 in 2 years, compounded annually?
(a) 4%
(b) 5%
(c) 6%
(d) 8%
(c) 6%
Here, $A=P \times\left(1+\frac{R}{100}\right)$
$=$ Rs. $7500 \times\left(1+\frac{R}{100}\right)^{2}$
$=$ Rs. $7500 \times\left(1+\frac{R}{100}\right)^{2}$
However, amount $=$ Rs. 8427
Now, Rs. $8427==$ Rs. $7500 \times\left(1+\frac{R}{100}\right)^{2}$
$\Rightarrow \frac{\text { Rs. } 8427}{\text { Rs. } 7500}=\left(1+\frac{R}{100}\right)^{2}$
$\Rightarrow\left(\frac{53}{50}\right)^{2}=\left(1+\frac{R}{100}\right)^{2}$
$\Rightarrow\left(1+\frac{R}{100}\right)=\left(\frac{53}{50}\right)$
$\Rightarrow \frac{R}{100}=\frac{53}{50}-1$
$\Rightarrow \frac{R}{100}=\frac{53-50}{50}=\frac{3}{50}$
$\therefore R=\frac{300}{50}=6 \%$