Question : If the compound interest on a certain sum for 2 years at 4% per annum is Rs. 102, the simple interest on the same rate of interest for two years would be:
Option 1: Rs. 200
Option 2: Rs. 50
Option 3: Rs. 150
Option 4: Rs. 100
Correct Answer: Rs. 100
Solution :
Given:
Compound Interest = Rs. 102
Rate = 4% per annum
Time = 2 years
When compounded annually, Compound interest $CI= P(1+\frac{R}{100})^{T}-P$, 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.
So, $102=P(1+\frac{4}{100})^{2} - P$
⇒ $102=P(\frac{26}{25})^{2} - P$
⇒ $102=P[(\frac{26}{25})^{2}-1]$
⇒ $102=P[\frac{676-625}{625}]$
⇒ $102×625=51P$
$\therefore P=1250$
Required simple Interest $=\frac{\text{Principal × Rate × Time}}{100} = \frac{1250 \times 4 \times 2}{100} = 100$
Hence, the correct answer is Rs. 100.
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