This equation calculates the future value of an annuity, reporting the future value of some set of n payments to an investment account which earns an interest rate (r) at each period.

Inputs

The inputs are:

• P - the fixed payment amount
• r -   the fixed periodic interest rate
• n - the number of compounding periods over which the fixed payments are made

The future value of these payments is output.

Description

This equation computes the accumulated amount you will have after some number of fixed payments is made to an account that is earning compound interest at a fixed interest rate.

Usage

Monthly Interest Example

An example where the compounding period would be months is as follows:

If you made monthly payments (so your periodic rate is a monthly rate) to an interest-earning account, where:

• the number of monthly payments was 36  (n = 36) 
• the payment amount is a fixed amount of $100 each month (P = 100)
• the fixed interest rate is 1.5% per month (r = 1.5)

The resulting Future Value in that account at the end of 36 months would be: $4727.60

Loan Shark Example

If you ran a fictional loan shark business and wanted to compute the future value of a loan of 5,000 to a "client" using a daily compounding period you might have an example like this:

• the number of daily payments due is 10 (n = 10)
• the payment amount is a fixed $500 on a $5,000 original loan (P = 500)
• the fixed interest rate quoted to the client in a very loud voice is 25% per day (r = 40)

If the client only manages to pay you $500 each day for ten days, this equation tells you that you the future value (after ten days) of you loan, including interest, would be $16,626.45.  That means your client had better bring an extra $11,626.45 on the tenth day if he wants the loan to be paid off.  Maybe Bruce Willis should play the client.

See also

Future Value (Ordinary Annuity)