*Compound interest is the concept* of earning interest on your investment,
then earning interest on your investment plus the interest. Over time this
results in the exponential growth of your money. The longer your investment
stays in the account, the greater the ratio of interest to the original
amount.

This compound interest calculator demonstrates the power of compounding interest by graphically showing the value of your investment, broken down into the principal, any monthly deposits and the accumulated interest earned.

Javascript is required.

- Final Balance
- Total Deposits
- Total Interest

Joe’s brother has just had a new baby, Emily. Joe decides that he would like to set up a savings vehicle in Emily’s name, to provide a nest egg for her when she is older. He knows how hard it is to save up money for a deposit on a mortgage, and wants to make it easier for Emily when she gets to that time on her life.

Joe finds a long term savings account offering a rate of 4.2% effective annual interest rate (eAPR). He decides to put $1,000 into the account to open it, and to set up an automatic deposit of $50 per month from his regular bank account.

Wondering how much this will amount to when Emily is 30 he enters $1000 into the Principal field, $50 into the Monthly Deposit field, 4.2 into the % Rate field, and 30 into the Years field.

Hitting the Calculate button brings up the results of the savings calculator. After 30 years the final balance will be $39,484. Of this, $18,000 is from the $50 monthly deposits he made. The remaining $20,484 is the interest which accrued in the account over the years.

Joe plays around with the principal and monthly deposits to get a feel for how different inputs will affect the outcome. He notices that over such a long period, it is the size of the regular monthly payments that has the biggest effect on the final balance.

For instance, increasing his monthly contribution from $50 to $60 results in a final balance $7,000 higher than the smaller $50 contribution. He decides he can afford the extra $10 a month and resolves to increase his monthly deposit.

He also notes that the interest portion outweighs the amount he contributes. Looking at the ratio between interest and deposits (the green part of the chart compared to the yellow part), he sees that initially interest plays very little part in the growth. After 6 years, his deposits total $4,320, and the interest paid only $869. But as time goes on, the interest mounts up. By the 30th year, the interest totals $24,000, moving ahead of the deposits of $21,600 for the first time.

A mathematical formula for calculating compound interest (as used by this online calculator), can be stated as:

V = P ( 1 + [ r / n ] ) ^ n * t

where:

- V = the value of investment at the end of the time period
- P = the principal amount (the initial amount invested)
- r = the annual interest rate
- n = the annual frequency of compounding (how many times a year interest is added)
- t = the number of years the money is invested
- ^ means raise to the power of

For instance, investing $1,000 for 20 years at a rate of 7.2% where the interest is compounded monthly, results in:

V = 1000 * (1 + [0.072 / 12]) ^ (12 * 20) = 4202.57

So the value of the investment at the end of 20 years will be $4,202.57. The total interest earned is found by subtracting the principal from the final value, in this case:

4,202.57 - 1000 = $3,202.57