Question : What is the difference (in INR) between the interests on INR 50,000 for one year at 8% per annum compounded half-yearly and yearly?
Option 1: 80
Option 2: 100
Option 3: 70
Option 4: 50
Correct Answer: 80
Solution :
Principal, $P = 50000$
Term, $n = 1$ year
Rate, $R = 8$%
When compounded half-yearly,
Compound Interest, CI = $P(1+\frac{R}{200})^{2n}-P$
= $50000 × (1+\frac{8}{200})^2 - 50000$
= $50000 × (\frac{208}{200})^2 - 50000$
= $50000 × (\frac{26}{25})^2 - 50000$
= $50000 × \frac{676}{625} - 50000$
= $54080 - 50000$
= $4080$
When compounded annually,
Compound Interest, CI = $P(1+\frac{R}{100})^{n}-P$
= $50000 × (1+\frac{8}{100})^1 - 50000$
= $50000 × \frac{8}{100}$
= $4000$
So, the required difference $=4080 - 4000=$ INR $80$
Hence, the correct answer is 80.
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