How compound interest works
With compound interest you earn interest on your interest. Each period, the interest earned is added to the balance, and the next period's interest is calculated on that larger balance. Over long periods this is what makes savings and investments grow faster than a straight line.
The compound interest formula
For a single deposit with no further contributions:
A = P × (1 + r ÷ n)n × t
A is the final amount, P the starting amount, r the yearly rate as a decimal, n the number of compounding periods a year and t the number of years. With regular monthly deposits, each deposit grows for a shorter time, so the calculator adds them month by month.
Worked example: $10,000 plus $200 a month at 5% compounded monthly grows to $47,526.55 after 10 years. You deposit $34,000 in total, so $13,526.55 is interest.
APY, AER and the effective rate
Banks quote savings rates in two ways. The nominal rate is the headline yearly rate. The effective rate, called APY in the US and AER in the UK, shows what you actually earn in a year once compounding is included:
Effective rate = (1 + r ÷ n)n − 1
| Compounding | Effective rate at 5% nominal |
|---|---|
| Yearly | 5.000% |
| Quarterly | 5.095% |
| Monthly | 5.116% |
| Daily | 5.127% |
Pro-tip: compare savings accounts by APY or AER, never by the nominal rate. The difference between monthly and daily compounding is small; the difference between two banks' rates usually matters far more.
Limitations: the calculator assumes a constant rate and ignores tax and inflation. In the UK, interest inside an ISA is tax-free; in the US, a Roth IRA or 401(k) changes the tax picture; in Canada, a TFSA does. Investment returns are not guaranteed, and past growth does not predict future growth.
Frequently asked questions
What is the formula for compound interest?
A = P × (1 + r ÷ n)^(n × t), where P is the starting amount, r the yearly rate, n the compounding periods per year and t the number of years.
What is the difference between APY and AER?
They are the same idea. APY (annual percentage yield) is the US term and AER (annual equivalent rate) is the UK term. Both show the effective yearly rate after compounding.
Does daily compounding make a big difference?
Not much. At 5%, monthly compounding gives an effective 5.116% and daily compounding 5.127%. The rate itself matters far more than how often it compounds.
How long does it take to double my money?
A quick estimate is the rule of 72: divide 72 by the yearly rate. At 6%, money doubles in about 12 years. The calculator gives the exact figure.