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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value

An investment requires an outlay of Rs 1,000 now and pays Rs 600 at the end of year 1 and Rs 600 at the end of year 2. What is the yield (internal rate of return) per annum, to two decimal places?

The yield is 13.07% per annum. Setting 1,000 equal to 600v plus 600v squared gives 5x squared minus 3x minus 3 equals zero, where x is one plus the interest rate. The positive root is 1.13066. Simple averaging of the total profit gives 10%, which ignores the timing of the returns.

  1. A9.54%
  2. B10.00%
  3. C13.07%Correct
  4. D15.47%
  5. 20.00%

Explanation

The equation of value is 1,000 = 600v + 600v^2. With x = 1+i this gives 5x^2 - 3x - 3 = 0, so x = (3 + sqrt(69))/10 = 1.13066 and i = 13.07%. Check: 600/1.13066 + 600/1.27839 = 530.65 + 469.34 = 999.99, matching 1,000 within rounding. The 10% option comes from averaging the total profit of 200 per year over the outlay and ignoring the timing of the cashflows.

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