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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting

An investment grows at a force of interest of 6% per annum for the first 3 years and then at a nominal rate of 9% per annum convertible half-yearly for the next 2 years. Rs 50,000 is invested at the start. What is the accumulated value at the end of 5 years, to the nearest rupee?

The accumulated value is about Rs 71,386. Growth over three years at force 6% is e^0.18 = 1.1972, and two years at 4.5% per half-year gives 1.045^4 = 1.1925; multiplying gives 1.4277 and Rs 50,000 grows to roughly Rs 71,386.

  1. ARs 71,641Correct
  2. BRs 70,889
  3. CRs 72,468
  4. DRs 73,115
  5. Rs 69,950

Explanation

First 3 years: e^0.18 = 1.197217. Next 2 years: 1.045^4 = 1.192519. Product = 1.427700; times 50,000 = 71,385. Computing: 1.197217 x 1.192519 = 1.42773, giving about Rs 71,386, which matches no option exactly, so the key is the closest listed value is wrong; the correct figure is Rs 71,386.

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