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How to Calculate the Present Value of an Annuity

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  • 0:01 Annuity
  • 0:31 Present Value
  • 0:58 Formula
  • 1:45 Example
  • 3:39 Lesson Summary
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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.

After watching this video lesson, you should know how to calculate how much an annuity is worth at any given time. Learn how to use the formula to calculate the current worth of an annuity that you may have.

Annuity

Sarah did really well when she was younger. She worked hard, and she saved her money. Now, in her older years, she is benefiting from her hard work. She now has an annuity that pays her every month. An annuity is an interest-bearing account that either pays you a fixed amount each month or that you pay into each month. Sarah's annuity account is one where she gets paid a fixed amount every month. Sarah benefits both from the monthly payments and the interest that is earned on the account.

Present Value

Sarah, being the hardworking person that she is, did her homework when she was looking at different annuity options from different banks. When she would go to a bank to ask about their annuity offerings, she would ask them for the present value of the annuity. This number lets her know the value of the annuity today. She didn't want to know how much her annuity will be worth in the future. She wanted to know its worth as of right now.

Formula

At each bank, she would also ask for the particulars of the annuity such as the fixed payment amount, the interest rate, and the number of payments. She knew what particulars to ask for because she remembers from her math classes in high school the formula that is used to calculate the present value of an annuity. She knew it would come in handy for her later on in life, so she made sure to remember it. The formula that she remembered is this one:

present value

In this formula, the P represents the fixed payment amount, the i the interest rate, and n the number of payments. Sarah also remembers that if the payments are made monthly and we are given an annual interest rate from the bank, then we would need to divide that annual interest rate by 12 to find the monthly interest rate to use in the formula.

Example

Let's see how Sarah uses this formula to calculate the present value of her annuity. The particulars of her annuity are a fixed payment of $1,000, an annual interest rate of 12%, and a total of 60 monthly payments. This means that she is getting paid every month for 5 years. Also, since she is getting paid every month, Sarah needs to divide the interest rate by 12 to find the monthly rate.

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