### Problem

If you deposit 5,000 at the end of each year for 21 years into an investment account which pays an interest rate of 4% a year, what will the account balance be worth at the end of the 21 years?

### Solution

Payments of 5,000 (Pmt) are invested at the end of each year from the next 21 years (n), and each payment needs to be compounded forward to the end of year 21 at a discount rate of 4% (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 future value of an annuity formula as follows:

Pmt = 5,000 n = 21 i = 4% FV = Pmt x ( (1 + i)^{n}- 1 ) / i FV = 5,000 x ( (1 + 4%)^{21}- 1 ) / 4% FV = 159,846.01

### Explanation

The balance on the account after 21 years will be the same as the future value of the annual payments of 5,000 invested at the rate of 4% a year for 21 years.

### AN2 Annuity Examples

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