### Problem

An annuity that will pay 2,500 a year for 8 years. If the first payment is made today and the discount rate is 5%, what is the annuity worth today?

### Solution

Payments of 2,500 (Pmt) are received at the start of each year from the next 8 years (n), and each payment needs to be discounted back to the start of year 1 at a discount rate of 5% (i).

As the payments are made at the start of each year the annuity is an annuity due and the problem is solved using the present value of an annuity due formula as follows:

Pmt = 2,500 n = 8 i = 5% PV = Pmt x (1 + i) x (1 - 1 / (1 + i)^{n}) / i PV = 2,500 x (1 + 5%) x (1 - 1 / (1 + 5%)^{8}) / 5% PV = 16,965.93

### Explanation

The payments of 2,500 received at the start of each year for the next 8 years are each discounted back at the rate of 5% to give a present value of 16,965.93.

It follows from this that if considering buying an annuity, then it is worth paying 16,965.93 today to receive the annuity of 2,500 for the next 8 years if the discount rate is 5%.

### AN5 Annuity Examples

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