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.
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.
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.
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:
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.
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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She gets 0.12/12 = 0.01. She changed the percentage into a decimal to make the calculations. So, she has a monthly interest rate of 1%. She will use 0.01 in the formula. So, plugging in $1,000 for P, 0.01 for i, and 60 for n, she gets present value = 1,000 * ((1 - (1 + 0.01)^-60) / 0.01). Evaluating this, she gets present value = 1,000 * ((1 - (1.01)^-60) / 0.01) = 1,000 * ((1 - 0.5504496) / 0.01) = 1,000 * (0.44955 / 0.01) = 1,000 * 44.955 = 44,955.0384.
Rounding off to two decimal places, Sarah gets a present value of $44,955.04 for her annuity. So, this is how much her annuity with fixed monthly payments of $1,000 and an interest rate of 12% is worth today.
Let's see what we've learned. We learned that an annuity is an interest-bearing account that either pays you a fixed amount each month or that you pay into each month. The present value of an annuity is the value of the annuity today. To calculate the present value of an annuity, we use this formula:
The P stands for the fixed payment amount, the i stands for the interest rate, and the n stands for the number of payments. If the payments are made monthly and you are given an annual interest rate, then you will need to divide the annual interest rate by 12 to find the monthly interest rate before using the formula. To use this formula, you plug in your P, your i, and your n. You then evaluate to find your answer.
Upon completing this lesson, you should be able to:
Define annuity and present value
Identify the formula for calculating the present value of an annuity
Explain how to use the formula to calculate present value
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