IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
The relationship between the present value of an annuity-due and an annuity-immediate of the same term n and annual effective rate i is best stated as:
The annuity-due present value equals the annuity-immediate present value multiplied by (1+i), because every payment occurs exactly one year earlier and so is discounted one year less.
- Aa-due(n) = a(n) × (1+i)Correct
- Ba-due(n) = a(n) × (1+i)^n
- Ca-due(n) = a(n) / (1+i)
- Da-due(n) = a(n) + i
- a-due(n) = a(n) − 1 + v^n
Explanation
Each payment of the annuity-due is made one year earlier than the matching payment of the annuity-immediate, so each is worth (1+i) times as much at time 0. Hence a-due(n) = (1+i) a(n). Dividing by (1+i) would give the reverse relationship and is wrong.
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