The simple interest on a certain sum for $3\frac{1}{2}$ years at the rate of 10% per annum is ₹2,940. What will be the compound interest (in ₹) on the same sum for $1\frac{1}{2}$ years at the same rate when interest is compounded half-yearly (nearest to a rupee)?
Answer & explanation
Correct answer: option 1
Simple interest = \(\frac{P × R × T}{100}\)
2940 = \(\frac{P × 10 × 7}{100 × 2}\)
2940 = \(\frac{P × 7}{20}\)
P = Rs. 8400
When interest is compounded half yearly . Actual rate = \(\frac{10}{2}\)%
= 5%
Compound interest = Amount - Principal
= P$(1 \;+\; \frac{R}{100})^t$ - P
= 8400 [ 1 + \(\frac{5}{100}\) ]³ - 8400
= 8400 × \(\frac{21}{20}\) × \(\frac{21}{20}\) × \(\frac{21}{20}\) - 8400
= 9724.05 - 8400
= 1324.05
= 1324 ( nearest rupee )