Question:
At what rate percent will a sum of Rs 1000 amount to Rs 1102.50 in 2 years at compound interest?
Solution:
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$
$1102.50=1000\left(1+\frac{\mathrm{R}}{100}\right)^{2}$
$\frac{1102.50}{1000}=(1+0.01 \mathrm{R})^{2}$
$(1+0.01 \mathrm{R})^{2}=1.1025$
$(1+0.01 \mathrm{R})^{2}=(1.05)^{2}$
On comparing both the sides, we get:
$1+0.01 \mathrm{R}=1.05$
$0.01 \mathrm{R}=0.05$
$\mathrm{R}=5$
Thus, the required rate percent is 5 .
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