Question
A man invests ₹30,000 in a scheme offering compound
interest at 15% per annum, compounded half-yearly. Another man invests ₹35,000 in a scheme offering simple interest at 18% per annum. After 2 years, what is the difference in the total amounts received by the two men?Solution
For the first man (Compound Interest): Principal = ₹30,000, Rate = 15% per annum = 7.5% per half-year, Time = 2 years = 4 half-years. Amount = P × (1 + R/100)^T = 30,000 × (1 + 7.5/100)^4 = 30,000 × (1.075)^4 = 30,000 × 1.33547 = ₹40064. For the second man (Simple Interest): Principal = ₹35,000, Rate = 18%, Time = 2 years. Amount = P + (P × R × T / 100) = 35,000 + (35,000 × 18 × 2 / 100) = 35,000 + 12,600 = ₹47,600. Difference = ₹47,600 - ₹40064 = ₹7536 Correct option: e. ₹7536
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