IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
Payments of Rs 2,000 are due at time 2 years and Rs 3,000 at time 5 years. At 6% per annum effective, what single payment at time 4 years has the same value?
The equivalent payment is Rs 5,077.39. At time 4 the first payment has been accumulating for two years, giving 2,247.20, while the second payment is one year away and is discounted to 2,830.19. Adding the two gives the value.
- ARs 5,427.20
- BRs 5,000.00
- CRs 4,610.18
- DRs 5,077.39Correct
- Rs 4,917.19
Explanation
Value at time 4 = 2,000 × 1.06^2 + 3,000 × 1.06^-1 = 2,247.20 + 2,830.19 = Rs 5,077.39. Rs 5,427.20 accumulates the second payment instead of discounting it. Rs 4,610.18 discounts the first payment instead of accumulating it. Rs 4,917.19 discounts the second payment by two years.
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