Compound interest is interest earned on your interest. Each period, the growth is added to the balance, so the next period's growth is calculated on a bigger number. Over long stretches this does more of the work than your deposits do. This calculator shows the end balance, how much of it came from growth, and what you'd need to save monthly to reach a target.
How it works
A lump sum grows as P × (1 + i)ⁿ, where i is the rate per month and n is the number of months. Regular deposits grow as D × ((1 + i)ⁿ − 1) ÷ i, which adds up every deposit with the growth it earns until the end. Deposits are assumed at the end of each month.
Compounding frequency changes the effective rate slightly. A 7% rate compounded monthly earns a little more than 7% compounded once a year, because growth is added sooner. The calculator converts any frequency to an equivalent monthly rate so deposits and compounding line up.
For a goal, the formula runs in reverse: take the goal, subtract what your starting amount will grow to, and work out the monthly deposit that fills the gap.
These are nominal figures. Inflation reduces what the final balance will buy, and investment returns vary from year to year. Treat the result as a planning estimate, not a forecast. This is general information, not financial advice.
A worked example
You start with $10,000, add $500 a month and earn 7% a year compounded monthly. After 10 years you'd have about $106,639. You paid in $70,000, so about $36,639 is growth. To reach $100,000 in the same 10 years, you'd need to deposit about $462 a month, so you're on track.
Questions people ask
What is the formula for compound interest?
For a lump sum, A = P × (1 + r/k)^(k × t), where P is the starting amount, r the annual rate, k the number of compounding periods a year and t the number of years. Monthly deposits add a second term, D × ((1 + i)ⁿ − 1) ÷ i.
How much difference does compounding frequency make?
Less than most people expect. At 7%, monthly compounding gives an effective yearly rate of about 7.23%, and daily about 7.25%. The rate itself and the number of years matter far more.
What is the rule of 72?
Divide 72 by the annual rate to estimate how many years money takes to double. At 7% it's about 10 years; at 9% about 8. It's a quick mental check, not an exact figure.
Should I include inflation?
To see what the balance will buy in today's money, subtract expected inflation from the rate. For example, use 4% instead of 7% if you expect 3% inflation. The result is a rough real value.
Is this the same as a profit-sharing or Islamic savings account?
Islamic savings accounts pay an expected profit rate that can change, rather than fixed interest. Entering the expected rate gives an estimate of growth, but actual profit depends on the bank's results.