IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
A project costs Rs 5,00,000 and yields Rs 1,00,000 at the end of each year for as long as required. At an effective annual rate of 8%, what value of n solves a-angle-n (the annuity-immediate present value) equal to 5, i.e. the exact discounted payback period treating n as continuous?
The exact discounted payback period is 6.64 years. Setting the annuity value (1 - v^n)/0.08 equal to 5 gives v^n = 0.6, so n = ln(1/0.6) divided by ln(1.08), which equals about 6.64.
- A5.00 years
- B6.25 years
- C6.64 yearsCorrect
- D7.00 years
- 8.33 years
Explanation
We need (1 - v^n)/0.08 = 5, so v^n = 0.6. Then n = ln(1/0.6)/ln(1.08) = 0.510826/0.076961 = 6.64. Answering 5.00 is the simple payback, which ignores interest. Answering 7.00 rounds to the next whole payment date rather than solving for n.
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