The compound interest formula
Compound interest means you earn interest on your interest. The classic formula for a single deposit is A = P × (1 + r/n)^(n × t), where P is the starting amount, r is the annual rate as a decimal, n is the number of times interest compounds per year and t is the number of years. $1,000 invested at 5% compounded annually for 10 years grows to $1,628.89. With monthly compounding it becomes $1,647.01, and with daily compounding $1,648.66.
Regular contributions add a second part. If you deposit an amount at the end of every month, each deposit grows for a shorter time than the one before. Depositing $100 a month for 10 years at 6% compounded monthly builds $16,387.93, of which $12,000 is your own money and $4,387.93 is interest.
How this calculator handles contributions
The calculator steps through every month. Each month it grows the balance by the monthly equivalent of your chosen compounding frequency and then adds your contribution. This gives exact results for monthly compounding and accurate results for daily, quarterly and annual compounding, where contributions earn the equivalent effective rate. The yearly table shows how much you have contributed and the balance at the end of each year, so you can see the point where interest begins to outpace your deposits.
The power of time
Because growth builds on itself, time matters more than almost anything else. At a 7% return, money roughly doubles every 10 years; the rule of 72 says divide 72 by the rate to estimate the doubling time. Someone who invests $200 a month from age 25 to 65 at 7% ends up with about $525,000. Someone who starts at 35 needs to invest roughly $430 a month, more than double, to reach the same amount by 65. Starting early, even with small amounts, is the single biggest lever most savers have.
APY, inflation and real returns
Banks quote the annual percentage yield (APY) on savings accounts because it includes compounding; the calculator shows the APY for your rate and frequency. Investment returns are not guaranteed. Stock markets have historically averaged around 7% a year after inflation over long periods, but individual years range from large losses to large gains. Inflation also erodes buying power: at 3% inflation, prices double in about 24 years. To estimate real growth, subtract expected inflation from your rate. Taxes and fees reduce returns too, so tax-advantaged accounts and low-cost funds can make a large difference over decades. Run the calculator with a cautious rate as well as an optimistic one to see a realistic range of outcomes.
Frequently asked questions
What is the formula for compound interest?
A = P × (1 + r/n)^(n × t), where P is the principal, r the annual rate, n the compounding periods per year and t the number of years.
Does compounding frequency matter much?
It matters a little. Moving from annual to monthly compounding adds a small amount; moving from monthly to daily adds even less. The rate and time invested matter far more.
What is the rule of 72?
Divide 72 by the annual interest rate to estimate how many years it takes money to double. At 8%, it doubles in about 9 years.
Are the results guaranteed?
Only for fixed-rate products such as CDs. Investment returns vary from year to year, so treat projections as estimates.