How Do You Calculate Present Value in an Annuity?

The example in the text book on present value asks how much would you need to deposit today to end up with $2,000,000? The example on the homework is easier.

Problem Find the present value of an ordinary annuity with payments of $10,000 paid semiannually for 15 years at 5% compounded semiannually.

Solution We’ll use the formula

to find the present value PV. Think of this as a decreasing annuity problem where we want the future value to be zero. From the problem statement, we know that



Put these values into the formula and solve for PV:


If we evaluate this in a graphing calculator, we get approximately $209,302.93. It might be easier to evaluate the top and bottom of this fraction first, and then to divide the results. If you do this, be careful to not round those pieces…only round at the end after you divide.