What compound interest means
Simple interest pays you only on the money you put in. Compound interest pays you on your deposits and on the interest already earned, so growth speeds up over time. In the early years most of your balance is your own contributions. Given enough time, the interest line in the table overtakes them, and that is when compounding starts doing the heavy lifting.
The formula
For a single deposit with no additions, the future value is:
A = P × (1 + r/n)n×t
P is the starting amount, r the annual rate, n the number of compounding periods per year and t the number of years. $10,000 at 5% compounded annually for 10 years grows to $16,288.95. Compounded monthly, it becomes $16,470.09.
With monthly contributions the calculator converts the rate to an equivalent monthly rate, (1 + r/n)n/12 − 1, and adds each deposit at the start or end of the month. That handles any combination of compounding frequency and monthly deposits correctly.
Why compounding frequency matters less than you think
Going from annual to monthly compounding adds a little, and going from monthly to daily adds even less. The effective annual yield line shows the difference: 5% compounded daily is about 5.127% a year, versus 5.116% monthly. The rate itself, how much you add each month and especially how many years you leave the money alone matter far more.
The rule of 72
A quick mental check: divide 72 by the annual rate to estimate how many years it takes money to double. At 6% that is about 12 years; at 9% about 8 years. It is an approximation, but it shows why starting a decade earlier can matter more than contributing a larger amount later.
Picking a realistic rate
High-yield savings accounts and CDs pay a stated APY that changes with interest rates. Stock market returns are not guaranteed and vary a lot from year to year, so long-term projections often use a conservative average. If you want results in today's dollars, subtract expected inflation from the rate (for example, 7% minus 3% gives a 4% "real" return) and the balance will be in today's purchasing power.
Frequently asked questions
How much will $10,000 grow in 10 years?
At 5% compounded annually it grows to $16,288.95. At 7% compounded monthly it reaches about $20,097. Adding monthly contributions increases the result substantially.
Is daily or monthly compounding better?
Daily compounding earns slightly more, but the difference is small: at 5% it is about 5.127% a year versus 5.116% for monthly compounding. Compare accounts by their APY, which already includes compounding.
What is the difference between APR and APY?
APR is the stated annual rate without compounding. APY is the effective yield after compounding within the year. For savings, APY is the number to compare.
Do contributions at the start of the month make a difference?
Yes, slightly. Money deposited at the start of the month earns one extra month of interest on every deposit, which adds up over many years.