# Lesson 2 - Value of Money - Part 3 Future Value of an Annuity

If we remember an Annuity is simply a series of equal reoccurring payments.  Investments and Insurance products often involve making these same kind of payments.  There are two kinds of Annuities that we will be discussing.

Ordinary Annuity

Annuity Due

Let’s say we have an investment that requires a \$1,000 payment made every year.  How much will we have after 4 years at an average of 5% return with each type of Annuity?

Ordinary Annuity

In an ordinary annuity it simply means we will be making the payment at the end.  In our case from above we will be making the payments at the end of every year.

Firstly we will break down the payments into the 4 years.  Our first payment would occur 1 year from now and would accumulate 3 years of interest.  Our second payment would occur 2 years from now and would accumulate 2 years or interest.  Our third payment would occur 3 years from now and accumulate 1 year of interest.  Our fourth and final payment would be made 4 years from now and would not accumulate any interest.

 First Payment \$1,000 x 1.05 x 1.05 x 1.05 = \$1,157 Second Payment \$1,000 x 1.05 x 1.05 = \$1,102 Third payment \$1,000 x 1.05 = \$1,050 Fourth payment \$1,000 x 1.00 = \$1,000 Total = \$4,309

Our investment would have made \$4,309 dollars. So \$1 dollar invested returns us \$4.309 in this investment. We have just calculated the Future Value of an Ordinary Annuity.

Let’s look and see what this investment would have done with the other type of Annuity, an Annuity Due.