Copyright

How to Find the Value of an Annuity

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Use the Binomial Theorem to Expand a Binomial

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:04 What Is an Annuity?
  • 0:50 The Formula
  • 1:27 Labeling Your Numbers
  • 2:43 Finding the Value of…
  • 3:36 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Login or Sign up

Timeline
Autoplay
Autoplay
Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Want to see how much money you will have in the future if you make a set payment every month towards your annuity? Then watch this video lesson for the formula and how to use it.

What is an Annuity?

An annuity, simply put, is a savings account that starts paying you back in the future. Sounds cool, doesn't it? You work hard when you are young and put your money towards an annuity, and when you get older, you can turn this annuity around so that it starts paying you! The way annuities work is that you put a set amount of money towards your annuity account every month. This account also pays you interest the whole time. Over time, your annuity grows in value. Once you reach a certain age, your annuity can then be turned around to pay you back a certain amount each month. One of the more important calculations with regard to these annuities is how much money you will have accumulated in the future if you make a certain fixed payment every month given a fixed interest rate. This is the calculation that we will be talking about in this video lesson.

The Formula

Of course we have a formula for calculating the future value of an annuity. That's the beauty of math! We have a formula for almost everything! So, here is our beautiful formula:

annuity

Looks a little bit complicated, doesn't it? But don't worry; once we start plugging in numbers and we start evaluating it, it gets easier and easier. The FV stands for the future value of the annuity. The PMT stands for the monthly payment you are making each month. The i stands for the interest rate. And finally, the n stands for the number of times the bank is going to pay you your interest.

Labeling Your Numbers

Now, let's look at how we can use this formula in a real-life scenario. Pretend that this annuity is yours. You are at the bank and you are sitting down with the banker. You are calculating how much money you will have in the future if you put $200 into the annuity every month. The banker tells you that his annuity has an annual interest rate of five percent. The bank compounds, calculates and pays you the interest on a monthly basis. You are calculating the future value after ten years.

We start by labeling our numbers. Right away we can label our $200 with PMT. Since the bank compounds or pays you interest every month, over a period of ten years, the bank will have made 10 * 12 payments or 120 payments. So our n is 120. The banker says that he pays the interest on a monthly period so an annual percentage rate of five percent calculates to a monthly interest rate of five percent divided by 12 or 0.05 / 12 = 0.004167. So our i is 0.004167. Now we have all our numbers labeled, and we can now plug these numbers into our formula.

annuity

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account
Support