### Problem

If an annuity will pay 10,000 a year for 7 years (with the first payment made one year from today), and the discount rate is 8%, what is the annuity worth today?

### Solution

Payments of 10,000 (Pmt) are received at the end of each year from the next 7 years (n), and each payment needs to be discounted back to the start of year 1 at a discount rate of 8% (i).

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

Pmt = 10,000 n = 7 i = 8% PV = Pmt x (1 - 1 / (1 + i)^{n}) / i PV = 10,000 x (1 - 1 / (1 + 8%)^{7}) / 8% PV = 52,063.70

### Explanation

The payments of 10,000 received at the end of each year for the next 7 years are each discounted back at the rate of 8% to give a present value of 52,063.70.

It follows from this that if considering buying an annuity, then it is worth paying 52,063.70 today to receive an annuity of 10,000 for the next 7 years if the discount rate is 8%.

### AN1 Annuity Examples

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