# Interactive graphical illustration of compound interest

### Matthew B. Cormier & Gary E. Davis

#### General compound interest formula

The general formula for the accumulated amount in an account with an initial deposit of at time t = 0, with annual compound interest rate r, and n compounding periods per year is

where t is the time in years.

The interactive graphic below allows you to gain a visual appreciation for this compound interest formula by varying the parameters r, n, t and the total time period for which interest is earned.

The principal at time t = 0 is arbitrarily set to 1, so the accumulated amount at t years is simply a multiple of if that value is taken to be different from 1.

#### Explanation of parameters in the graphic

“TotalYears” is the number of years in total for which the principal earns interest.

“AnnualPeriods” is the number of compounding periods per year.

“Rate” is the annual rate of compound interest.

“Years” is the number of years for which the account has currently earned interest.

“Accumulated amount” is the accumulated amount after a given number of years, as a multiple of the initial principal at year 0.

(It is assumed the initial principal at year 0 is 1, and then the accumulated amount at any given year is a multiple of that initial principal.)

#### Use of the graphic

The sliders set the values for the various parameters.

You can see the values of the parameters, and cycle through those values continuously, by clicking on the “+” button to the left of the slider.

The number of annual periods at which interest is compounded, ranging from 1 through 52, has the least effect on the accumulated amount at any time.