Future Value of an Ordinary Annuity Help Needed

[ziggy]

I need help with 2 questions on the above subject. I've looked all over my math book to find a formula, etc and i can't. It's driving me crazy!

1. Find the Future Value of an Ordinary Annuity of $8,000 at 2.5% compounded annually for 4 years.

2. Find the Future Value of an Ordinary Annuity of $5,500 at 8% compounded quarterly for 5 years.

Thanks

 

[tkhunny]

I learned some formulas, once. I haven't used them for at least a decade. I build them every time, since it requires me to know only one thing and not a whole bunch fo formulas. That one thing is called "Basic Principles". Learn it. Make it your friend. Unless you are being tested on formulas, simply forget they exist. Make your own.

"Find the Future Value of an Ordinary Annuity of $8,000 at 2.5% compounded annually for 4 years."

Let's assume payments are at the beginning of each year.

P = Annual Payment = $8000

i = 0.025, r = 1+i = 1.025

n = 4

That's all the definitions. Now build it.

\(\displaystyle P*r^{4} + P*r^{3} + P*r^{2} + P*r\)

You should have studied simple geometric series. If so, you will recognize this expression as just such an animal. With a little practice, you will be able to see the total of this sequence.

\(\displaystyle P*r^{4} + P*r^{3} + P*r^{2} + P*r = \frac{P*r - P*r^{5}}{1-r} = P*r\frac{r^{4}-1}{i}\)

Take some time to get familiar with it. You will never search for formulas again.

 

[ziggy]

Thanks for the quick reply! That makes total sense to me!!