Question

What is the difference between the compound interests on ₹10,000 for 2 years at 20% per annum compounded yearly and half-yearly?

• A. ₹241
• B. ₹233.33
• C. ₹400
• D. ₹4000

Answer 1

The correct option is A

₹241

Principal, P = ₹ 10,000
Time, n = 2 years
Rate of interest, R = 20% per annum

Amount after 2 years, when interest is compounded annually
$=P(1+\frac{R}{100}{)}^n=10000\times (1+\frac{20}{100}{)}^2=10000\times (\frac{12}{10}{)}^2=₹14400$

Compound Interest for 2 years, when interest is compounded yearly
= ₹(14400 - 10000)
= ₹4,400

Amount after 2 years when interest is compounded half-yearly
$=P(1+\frac{R}{200}{)}^{2n}=10000(1+\frac{20}{2\times 100}{)}^{2\times 2}=10000(1+\frac{10}{100}{)}^4=10000(\frac{110}{100}{)}^4=10000\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}=₹14641$

Compound Interest for 2 years when interest is compounded half-yearly
= ₹(14641 - 10000)
= ₹4641

Difference in Compound interest
= ₹(4641 - 4400)
= ₹241