IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
Rs 500 is invested at the start of each year for 4 years, with the first payment made now. At 8% effective per annum, what is the accumulated value at the end of year 4, that is, one year after the last payment?
The accumulated value is Rs 2,433.30. Payments at the start of each year earn interest for 4, 3, 2 and 1 years respectively, which is 500 times the annuity-due accumulation factor of 4.866601 at 8%.
- ARs 2,253.06
- BRs 2,433.30Correct
- CRs 1,788.55
- DRs 2,933.30
- Rs 2,000.00
Explanation
The accumulation is 500 × s-double-dot(4) = 500 × 1.08 × (1.08^4 − 1)/0.08 = 500 × 4.866601 = 2,433.30. Rs 2,253.06 is the immediate annuity value, which ignores the extra year of interest on each payment. Rs 1,788.55 is the present value of the annuity-due, not the accumulation.
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