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Algebra II Textbook26 chapters | 256 lessons

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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.

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.

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:

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.

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.

After plugging everything in, we can evaluate it now. We begin by performing the addition 1 + 0.004167. This gives us 1.004167. Next, we take this to the 120th power. This gives us 1.6470751. Now, we subtract one from it to get 0.6470751. We divide this by 0.004167 to get 155.2856. Lastly, multiplying this by 200 gives us a future value of $31,057.12 after ten years of making $200 monthly payments. That's not bad at all. That's enough money to buy a car!

Now that we've learned how to use the formula to find the future value of an annuity, let's review. An **annuity** is a savings account that starts paying you back in the future. You make monthly payments into your annuity to build up its future value. To calculate the future value of an annuity, we use the formula PMT times 1 plus *i* to the *n*th power minus 1 over *i*. The PMT stands for the monthly payments you are making, the *i* is the interest rate, and *n* is the number of interest payments the bank will make. To calculate the *i* from a given annual percentage rate, you divide it by the number of times the bank will pay during the year. If the bank pays monthly, then you divide the annual percentage rate by 12. The *n* stands for the number of times the bank will pay you interest. If you want the formula to find your future value after five years and the bank pays monthly, then your *n* will be 5 * 12 or 60. To use this formula, you label your numbers from the problem, plug them in, and evaluate.

Each section of this lesson could strengthen your ability to:

- Describe annuities and understand how they work
- Label numbers from an equation
- Recall the equation for and calculate the future value of an annuity

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Algebra II Textbook26 chapters | 256 lessons

- Introduction to Sequences: Finite and Infinite 4:57
- How to Use Factorial Notation: Process and Examples 4:40
- How to Use Series and Summation Notation: Process and Examples 4:16
- Arithmetic Sequences: Definition & Finding the Common Difference 5:55
- How and Why to Use the General Term of an Arithmetic Sequence 5:01
- The Sum of the First n Terms of an Arithmetic Sequence 6:00
- Understanding Arithmetic Series in Algebra 6:17
- Working with Geometric Sequences 5:26
- How and Why to Use the General Term of a Geometric Sequence 5:14
- The Sum of the First n Terms of a Geometric Sequence 4:57
- Understand the Formula for Infinite Geometric Series 4:41
- Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences 5:52
- Using Sigma Notation for the Sum of a Series 4:44
- Mathematical Induction: Uses & Proofs 7:48
- How to Find the Value of an Annuity 4:49
- Special Sequences and How They Are Generated 5:21
- Go to Algebra II: Sequences and Series

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