Annuity Formula


Here's our user friendly take on annuity formulas. Rather than hit you with lots of i's and n's straight away, we thought it would be good to let you see some typical annuity situations.

If the situations we describe are the same (or similar) to the ones you're interested in, you can click through to learn more about each annuity formula and see examples of how they can be used.

Annuity Formula


piggy bank annuity
Example 1
Q. Billy 'The Annuity' Kid invests $1000 at the end of each year for ten years. His investment pays a return of 6% a year. How much money will Billy have saved including interest at the end of year ten?

A. The value of Billy's annuity at the end of year ten is $13,180.79.

To find out how this is calculated, look at Annuity Formula for the Future Value of Regular Payments.





mr annuity toad
Example 2
Q. Mr Toad is very lucky. He is going to receive regular payments of $1000 at the end of each year for five years. With no inflation, the $5000 he receives in total will be worth $5000 in five years' time. If, however, inflation runs at 4% a year, how much will the $5000 be worth at today's value?

A. The value of the payments is $4451.82.

To find out how this is calculated, look at Annuity Formula for the Present value of Regular Payments.





little miss annuity
Example 3
Q. Little Miss Muffet is in her office, where she finds an internet bank account paying 6% interest annually.

She wishes to make regular payments to accumulate $5000 over a period of five years.

How much money will she need to invest each year?

A. She will need to invest $887 each year.

To find out how this is calculated, look at Regular Payments to Accumulate a Target Amount.





jack and jill annuity
Example 4
Q. Jack and Jill are considering using a $300,000 mortgage to buy a home. They intend retiring in 20 years, so the mortgage must be paid completely in that time. They are offered a mortgage of $300,000 with a fixed annual interest rate of 6%. They can afford to pay $2500 a month. Will Jack and Jill be able to afford the monthly mortgage payments?

A. This mortgage will cost $2149.29 each month, therefore it is affordable for them. To find out how this is calculated, look at Annuity Present Value - Interest and Capital Repayment.





piggy bank annuity
Example 5
Q. Mother Goose breaks into her piggy bank. With the $250,000 she finds there (it's a big piggy bank) she buys a lifetime annuity from an insurance company which pays her an annual income of $18,000. The company invests the money and obtains an annual return of 5%. If Mother Goose lives for another 20 years, will her annual income of $18,000 be fully funded by the $250,000 she gave to the insurance company?

A. The present value of all the payments Mother Goose will receive is $224,319.79. Therefore, her annual income is fully funded and the insurance company will make a profit. To find out how this is calculated, look at Present value of Regular Payments 2.





annuity formula jeff
Example 6
Q. Jeff has $400,000 invested in a savings account at 4% a year. If he takes an annual income of $30,000 from this account, how long will it be before he runs out of money?

A. Jeff will run out of money in 19.4 years. To find out how this is calculated, look at Number of Payments Funded by an Annuity.







More about Annuity Formulas

There are two basic types of annuity formula:

The Present Value Annuity Formula
Let's say you could receive a series of identical payments in the future, over a period of years. These payments could be in the form of payments from a pension annuity you have purchased. Inflation will erode the value of these payments. The present value annuity formula allows to add up the present value of these payments to see if it is worth buying an annuity. The formula also helps you assess the present value of coupon payments from a bond, say.

The Future Value Annuity Formula
Let's say you're going to make a regular cash investment - say monthly - over a period of time and be paid interest regularly. The future value annuity formula allows you to calculate how much money you'll have accumulated, including the interest (and reinvested interest) when the period of investment has ended.







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