IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
An investor receives Rs 100 at the end of each month for 2 years. The interest rate is 12% per annum nominal, convertible monthly. What is the present value of the payments?
The present value is Rs 2,124.34. With 12% nominal convertible monthly the rate per month is 1%, so the 24 monthly payments of Rs 100 form an immediate annuity with factor 21.2434 at 1% per month.
- ARs 2,145.58
- BRs 2,028.06
- CRs 2,400.00
- DRs 2,124.34Correct
- Rs 2,103.30
Explanation
The monthly rate is 1%. PV = 100 × (1 − 1.01^-24)/0.01 = 100 × 21.2434 = 2,124.34. Rs 2,145.58 treats payments as at the start of each month. Rs 2,028.06 wrongly uses 12% effective annually on Rs 1,200 per year. Rs 2,103.30 discounts the value by one extra month.
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