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

A sum of money doubles under simple interest at 8% per annum and, separately, under compound interest at 8% per annum effective. By how many years (to two decimal places) does doubling take longer under simple interest?

Doubling takes about 3.49 years longer under simple interest. Simple interest needs 12.5 years (1 + 0.08t = 2), while compound interest needs ln2 ÷ ln1.08 ≈ 9.01 years, so the difference is 12.50 − 9.01 ≈ 3.49 years.

  1. A12.50
  2. B9.01
  3. C4.50
  4. D3.49Correct
  5. 2.49

Explanation

Simple: 1 + 0.08t = 2 gives t = 12.5 years. Compound: t = ln2/ln1.08 = 0.693147/0.076961 = 9.0065 years. Difference = 3.4935, i.e. 3.49 years. 12.50 and 9.01 are the individual times, not the difference.

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