IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
Rs 2,000 is deposited at the start of each year for 10 years into an account earning 7% effective annual interest. What is the accumulated value at the end of year 10, immediately after the last year's interest is credited?
The accumulated value is Rs 29,567.20. Deposits are made at the start of each year, so the accumulation is 2000 × s̈10 = 2000 × (1.07^10 − 1)/d with d = 0.07/1.07. Using the year-end annuity factor would understate it at Rs 27,632.90.
- ARs 15,030.46
- BRs 20,000.00
- CRs 27,632.90
- DRs 29,567.20Correct
- Rs 31,567.20
Explanation
The accumulated value is 2000 × s̈(10) = 2000 × (1.07^10 − 1)/d, where d = 0.07/1.07. This is 2000 × 0.967151/0.0654206 = 2000 × 14.7836 = Rs 29,567.20. Rs 27,632.90 treats deposits as made at year end, which omits one year's interest on every deposit.
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