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 ₹)
Answer & explanation
Correct answer: option 2
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.)