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How do you Calculate Annuities?

How do you Calculate the Value of an Annuity?

An annuity can be valued as a present value or a future value.

You can calculate the present value of an annuity or the future value of an annuity using a formula or on a calculator.

It is important to understand the formula to be able to understand the way to do your calculation.

Here are the basic formula to perform the calculations. Remember calculate the ‘factor’ then times it by the annuity amount.

How do you Calculate Annuities?

The formula to calculate an annuity is more complicated than calculating the value of a single sum.

This formula calculates the ‘annuity interest factor’. Multiply this by the annuity amount.

present value of an annuity
Present Value of Annuity Interest Factor where i = interest rate, n = number of periods

Future Value of an annuity
Future Value of an Annuity Interest Factor where i = interest rate, n = number of periods

Use your calculator or a phone calculator app to work out the calculations.

Turn your iPhone sideways for the full financial calculation options.

Use the circled function to do the calculation.

Try some calculations with this interactive financial maths spreadsheet Return to Financial Mathematics Questions and Answers

Now some examples of annuity calculations;

John is to receive $10,000 cash at the end of each year for the next 5 years. So this is an annuity. The interest rate is 12% annually.

Use the following formula to calculate the interest factor.  Multiply this by the annuity amount.

 where,

P is the periodic payment, i is the interest rate and n is the number of periods.

The formula for 5 years at 12% will give the PVAIF(i,n) = 3.6048

The present value of the annuity is $10,000 x PVAIF(i,n) = $10,000 x 3.6048

The present value of the annuity is 10,000 x 3.6048 = $36,048

Here is another example;

Bank loan calculations use the annuity formula.

The customer is getting the loan now (in year 0) which is the present value.

The calculation finds the repayment amount the borrower has to make to the bank. This is the annuity.

bank loan present value