IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
Which statement about the present value of Rs 1 due in n years at a constant effective annual rate i > 0 is correct?
The present value of Rs 1 due in n years is v to the power n, where v is 1 divided by 1 plus i. It falls as either i or n rises, because the payment is discounted more heavily.
- AIt increases as n increases
- BIt equals (1 - i)^n
- CIt equals v^n where v = 1/(1+i), and falls as i risesCorrect
- DIt is independent of i
- It equals 1 - n x i
Explanation
Present value of Rs 1 due in n years is v^n with v = 1/(1+i). A larger i makes v smaller, so the present value falls. It also decreases with n. (1-i)^n and 1-ni are not the discount factor under compound interest.
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