Lesson 2 - Value of Money - Part 4

Future Value of an Annuity

Annuity Due

In an Annuity Due, our payments are made at the beginning. In our example situation it means we will pay the $1,000 at the beginning of the year. We should start to see mentally that this investment will provide us more interest. In an Ordinary Annuity the payment didn’t start earning interest until the next year. However, in and Annuity Due the payment starts earning interest right away.

This means that we will get one more year of interest payments in our example, let’s take a look as we break down what each payment will earn.

(Just a reminder of the problem)
“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?”

First Payment $1,000 x 1.05 x 1.05 x 1.05 x 1.05 = $1,214
Second Payment $1,000 x 1.05 x 1.05 x 1.05 = $1,157
Third payment $1,000 x 1.05 x 1.05 = $1,102
Fourth payment $1,000 x 1.05 = $1,050
  Total  = $4,523

Our Annuity Due investment returned us $4,523 dollars. Our Ordinary Annuity only returned us $4,309 in the same time period, but in our Ordinary Annuity we were making payments at the end of the year. As a quick remembrance, an Annuity Due usually gets one more accumulation of interest.

Quick Method of Annuity Due = FVAD = (1.0 + i ) x FVOA
i being the interest rate in decimal form. --> FVAD = (1.0 + .05) x 4,309 = $4,523

If this Annuity example was for 40 years instead of 4, I hope we can see by now that the difference would be quite large. This is the power of earning interest over time. The more time we have the more powerful our interest payments can become. This is one of the main factors that we encourage young people to start saving for foundation goals early in life, even if it is only a little, it can add up to big amounts later on in life.


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