IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
Priya deposits Rs 10,000 at the start of each year for 5 years into an account earning 8% per annum effective. What is the accumulated value at the end of year 5, to the nearest rupee?
The accumulated value is about Rs 63,359. Deposits at the start of each year form an annuity-due, so the accumulation factor is (1.08^5 − 1)/d = 6.3359. Using the year-end annuity factor of 5.8666 would understate the fund by one year of interest.
- ARs 58,666
- BRs 63,359Correct
- CRs 68,423
- DRs 50,000
- Rs 54,000
Explanation
Accumulated value = 10,000 × s-due(5) = 10,000 × (1.08^5 − 1)/d, where d = 0.08/1.08 = 0.074074. 1.08^5 = 1.469328, so the numerator is 0.469328 and the factor is 6.3359. The result is 63,359. The value 58,666 is the annuity-immediate accumulation, which ignores that deposits are made at the start of each year.
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