Compound interest
See how one investment grows, and how much the compounding frequency changes the result.
About this calculator
What compounding actually does
Simple interest pays you on the original amount only. Compound interest pays you on the interest as well, so the base keeps growing and each period earns a little more than the last. Over short periods the difference is small; over decades it is most of the result.
The formula is A = P × (1 + r/n)^(n×t), where P is the amount invested, r the yearly rate, n how many times a year it compounds and t the number of years. The more often it compounds, the higher the final amount for the same quoted rate.
Why the frequency matters less than you think
Going from yearly to quarterly compounding makes a visible difference. Going from daily to continuous barely registers, because there is a limit to how much extra you can squeeze from the same rate. On 12% a year, yearly compounding gives an effective 12%, quarterly gives 12.55% and daily gives 12.75%. Beyond that it stops moving.
Time and the rate do the heavy lifting. Doubling the years changes the answer far more than changing the compounding frequency ever will.
Converting a rate between periods
The Convert a rate tab works in both directions. A rate for a month, a quarter or a week is added every period and compounds up: 1.5% a month is 18% if you only multiply by 12, but 19.56% a year once each month's interest earns interest.
A yearly rate is what the year ends with, so it is spread back instead. 12% a year is not 1% a month, because 1% a month compounds to 12.68%. The monthly rate that really matches 12% a year is 0.9489%.
A rough check: the rule of 72
Dividing 72 by the yearly rate gives roughly the number of years for money to double. At 8% that is about nine years; at 12% about six. It is approximate, but it is a quick sanity check on any projection someone shows you.
Common questions
What is the difference between simple and compound interest?
Simple interest is always calculated on the original amount. Compound interest is calculated on the amount plus the interest already earned, so the balance grows faster the longer it runs.
What does effective annual rate mean?
It is what a quoted rate actually works out to over a year once compounding is counted. A rate of 6% compounded monthly has an effective yearly rate of about 6.17%, which is the figure to use when comparing products that compound differently.
How long does it take to double my money?
Divide 72 by the yearly rate for a quick estimate. At 9% money roughly doubles in eight years. The calculator gives the exact figure for your rate and compounding frequency.
What is 1.5% a month as a yearly rate?
19.56% a year with monthly compounding, not 18%. Each month's interest earns interest in the months after it. Choose Month in the Convert a rate tab to see any rate this way.