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)?

1,324

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 )