Numerical: compound interest MCQ — 4 Practice Questions with Answers

Explanation

A 50% increase in 5 years at simple interest means the simple interest rate is 10% per annum. At the same rate, compound interest on ₹ 15,000 for 3 years is 15000[(1.10)^3 - 1]. Since 1.10 cubed is 1.331, the interest is 15000 × 0.331 = ₹ 4,965. ₹ 4,800 would be close to simple interest for a little over 3 years, not annual compounding. ₹ 4,900 and ₹ 4,960 are near values, but they do not follow the exact compound-interest calculation.

Explanation

With half-yearly compounding, 10% per annum becomes 5% per half-year. The amount after n half-years is 80,000 × (1.05)^n. Since 92,610 ÷ 80,000 = 1.157625, and (1.05)^3 = 1.157625, n is 3 half-years. That is 1½ years. One year would mean only two half-years, giving less. Two years and three years would mean four and six half-years, giving amounts higher than ₹ 92,610.

Explanation

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.

Explanation

Under compound interest, the amount from year 3 to year 6 is multiplied by the same 3-year growth factor. Thus the factor is 10,035 ÷ 6,690 = 1.5. The amount after 3 years is therefore 1.5 times the original sum, so the principal is 6,690 ÷ 1.5 = ₹ 4,460. ₹ 4,400 gives only ₹ 6,600 after that factor, ₹ 4,900 gives ₹ 7,350, and ₹ 5,000 gives ₹ 7,500, so those amounts do not fit the given 3-year amount.