Annuity Calculation - the Basics

In the compound interest formula shown:

• P = present value of a sum of money (in this case A_n)
• A_n = the sum of money after n time periods
• r = rate of interest per time period
• n = number of time periods

For the annuity calculation, take the payments in reverse order. The last payment A at the end of the time period (year n) will earn no interest so the value of the last payment will still be A in the end.

• The previous payment will earn one year's interest at the rate of interest of r so it will grow to A(1+r)
• The one before will grow to A(1+r)², and so on
• The first amount will be A(1+r)^n-1.

The total amount accumulated by the end of the nth year will be:

To simplify the above annuity calculation expression, we have:

Now that we have this expression for the annuity calculation of A_n, we derive the annuity formula. Click here for explanation of the annuity formula used in this annuity calculation.