IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Allowing for inflation
A perpetuity pays Rs 50,000 at the end of the first year, and each later annual payment increases in line with inflation of 4% per year. The effective annual interest rate is 9%. What is the present value?
The present value is Rs 1,000,000. For a perpetuity whose first payment is one year away and which grows at a constant rate, the value is the first payment divided by the interest rate minus the growth rate, 50,000 divided by 0.05.
- ARs 555,556
- BRs 384,615
- CRs 1,000,000Correct
- DRs 1,090,000
- Rs 1,040,000
Explanation
The payments grow at a constant rate g = 4% with the first payment one year away. PV = 50,000/(i - g) = 50,000/0.05 = Rs 1,000,000. Using 50,000/0.09 ignores the growth and gives Rs 555,556. Multiplying by 1.09 or 1.04 wrongly shifts the timing of the first payment.
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