The simple interest on a certain sum for 3 years at 12% p.a. is ₹6,750. What is the compound interest(in ₹) on the same sum for 2 years at 20% p.a., if interest is compounded half-yearly? (rounded off to the nearest ₹)

8,702

From the formula of simple interest . We know,

Simple Interest = \(\frac{P × R × T }{100}\)

6750 = \(\frac{P × 12 × 3 }{100}\)

6750 = \(\frac{P × 3 × 3 }{25}\)

P = 18750

Now,

From the formula for compound interest, we know,

C.I = P(1+$\frac{R}{100})^t$– P

Interest is compounded half yearly .

So, Actual rate = \(\frac{20 }{2}\)% = 10%

Actual time = 2 × 2 = 4 half years

C.I = 18750(1+$\frac{10}{100})^t$– 18750

= 18750 × \(\frac{11 }{10}\) × \(\frac{11 }{10}\) × \(\frac{11 }{10}\) × \(\frac{11 }{10}\) - 18750

= 27451.875 - 18750

= 8701.875

= 8702   ( Approx.)