Question : At what percentage rate, compound interest compounded annually for a sum of Rs. 40,000, will amount to Rs. 44,100 in two years?
Option 1: 5%
Option 2: 2%
Option 3: 4%
Option 4: 7.5%
Correct Answer: 5%
Solution :
When compounded annually, $ A= P(1+\frac{R}{100})^{T}$,
Where $A$ is the total amount, $P$ is the principal amount, $R$ is the rate of interest per annum, and $T$ is the time in years.
According to the question,
$⇒44100=40000(1+\frac{R}{100})^{2}$
$⇒(1+\frac{R}{100})^{2}=\frac{44100}{40000}$
$⇒(1+\frac{R}{100})^{2}=\frac{441}{400}$
$⇒\frac{R}{100}=\frac{21}{20}-1$
$⇒\frac{R}{100}=\frac{1}{20}$
$\therefore R=5\%$
Hence, the correct answer is 5%.
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