IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
Tata Capital pays Rs 10,000 at the end of each year for 5 years. At an effective annual rate of 10%, the present value of this annuity-immediate is Rs 37,907.87 (to the nearest paisa). What is the present value if the same payments are instead made at the start of each year?
The annuity-due present value is Rs 41,698.66, found by multiplying the annuity-immediate value of Rs 37,907.87 by 1.10, since each payment is made a year earlier and is discounted one year less.
- ARs 34,461.70
- BRs 41,698.66Correct
- CRs 47,907.87
- DRs 37,907.87
- Rs 45,489.44
Explanation
Annuity-due PV = 1.10 × 37,907.87 = 41,698.66. Option 34,461.70 divides by 1.10, which shifts payments in the wrong direction. Rs 47,907.87 adds a single payment of 10,000 instead of adjusting for interest.
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