Numerical: Compound Interest MCQ - Practice Questions with Answers

Under compound interest, the growth from year 4 to year 8 is one more 4-year compounding block. Therefore, the 4-year growth factor is ₹ 29,856 divided by ₹ 7,464, which is 4. The amount after 4 years is thus four times the original principal. Dividing ₹ 7,464 by 4 gives ₹ 1,866. ₹ 3,732 would be only half of the 4-year amount, ₹ 933 would make the 4-year amount eight times the principal, and ₹ 37,320 is larger than even the 8-year amount, so none of them can be the original sum.

At 10% compounded annually for 2 years, the amount factor is (1 + 10/100)^2 = (11/10)^2 = 121/100. So the compound interest factor is 121/100 − 1 = 21/100. Thus CI = 21% of the principal. For ₹5,000, CI = ₹1,050; for ₹6,000, CI = ₹1,260; for ₹7,000, CI = ₹1,470. Therefore the correct matching is 1-₹1,050, 2-₹1,260, 3-₹1,470. This is option A.

When interest is compounded half-yearly, the annual rate is halved and the number of periods is doubled. So 20% per annum becomes 10% per half-year, and 1 year gives 2 periods. Amount = 10000 × (1 + 10/100)^2 = 10000 × 1.21 = ₹12100. Compound interest = 12100 − 10000 = ₹2100. This is ₹100 more than simple interest because the second half-year earns interest on the first half-year's ₹1000 interest.

In the first year, interest = 10% of 12,000 = ₹1,200, so the amount becomes ₹13,200. In the second year, interest = 10% of 13,200 = ₹1,320. Total compound interest = 1,200 + 1,320 = ₹2,520, and the final amount is ₹14,520. Therefore, the statement saying the compound interest is ₹2,400 is incorrect; ₹2,400 is only the simple interest.

First year interest = 5% of 4000 = ₹200, so the amount becomes ₹4200. In the second year, interest is calculated on ₹4200, not on ₹4000. Second year interest = 5% of 4200 = ₹210. Final amount = 4200 + 210 = ₹4410, so compound interest = 4410 − 4000 = ₹410. Therefore the statement saying that the compound interest is ₹400 is incorrect; ₹400 is only the simple interest for 2 years.