IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
A contract pays Rs 10,000 at the end of each of the next three years. Using an effective annual interest rate of 10%, what is the present value of these payments?
The present value is Rs 24,868.52. Each end-of-year payment of Rs 10,000 is discounted by 1.10 raised to the payment year, and the three discounted values are added. Treating the payments as made at the start of each year gives a higher figure and is wrong.
- ARs 24,868.52Correct
- BRs 27,355.37
- CRs 30,000.00
- DRs 24,000.00
- Rs 23,000.00
Explanation
PV = 10,000(1/1.1 + 1/1.21 + 1/1.331) = 10,000(0.909091 + 0.826446 + 0.751315) = 24,868.52. Rs 27,355.37 is the annuity-due value, which wrongly treats payments as made at the start of each year. Rs 30,000 ignores discounting.
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