How compound interest works
With compound interest, each period's interest is added to the balance, so the next period's interest is calculated on a bigger number. Over long periods, that makes growth speed up.
Balance = P × (1 + r ÷ n)n × t
P is the starting amount, r is the yearly rate as a decimal, n is how many times a year interest is added, and t is the number of years. Monthly contributions are added at the end of each month and then earn interest too.
The effective yearly rate shows what the rate is worth after compounding. 7% compounded monthly works out to about 7.23% a year. It's the fairest way to compare accounts that compound differently.
This is the maths for a fixed rate. Real investment returns go up and down, and taxes or fees reduce them.
Questions people ask
Does compounding more often make a big difference?
Less than people expect. At 7%, yearly compounding gives 7% a year and daily compounding gives about 7.25%. The rate and the time matter much more.
What's the rule of 72?
A quick estimate: divide 72 by the interest rate to get roughly how many years it takes money to double. At 7%, that's about 10 years, which this calculator confirms.
Are the contributions added at the start or end of the month?
At the end. Contributions made at the start of each month would earn slightly more, because each one gets one extra month of interest.