IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
An annual effective interest rate is 10%. What is the present value today of Rs 5,000 payable at the end of each of the next 3 years?
The present value is Rs 12,434.26. The annuity-immediate factor for three years at 10% is (1 minus 1.1 to the power minus 3) divided by 0.1, which is 2.486852, and this is multiplied by 5,000. Annuity-due timing would overstate the value.
- ARs 12,434.26Correct
- BRs 15,000.00
- CRs 13,675.69
- DRs 12,000.00
- Rs 11,303.87
Explanation
v = 1/1.1. a3 = (1 - 1.1^-3)/0.1 = 2.486852. Multiplying by 5,000 gives 12,434.26. The 13,675.69 option is the annuity-due value, which wrongly assumes payments at the start of each year.
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