Compound Interest Calculator
How compound interest works
With compound interest, the interest you earn is added to your balance and earns interest itself the following year. Over long periods this "interest on interest" becomes the largest part of the final amount. For a single deposit compounded once a year:
Final amount = P Ć (1 + r)įµ
where P is the starting amount, r the annual rate (5% = 0.05) and t the number of years. If you also add a fixed contribution C at the end of each year, the contributions grow to C Ć ((1 + r)įµ ā 1) Ć· r, which the calculator adds for you.
Worked example
ā¬10,000 invested at 5% a year:
| After | Balance | Interest earned |
|---|---|---|
| 10 years | ā¬16,289 | ā¬6,289 |
| 20 years | ā¬26,533 | ā¬16,533 |
| 30 years | ā¬43,219 | ā¬33,219 |
With simple interest, the same ā¬10,000 would earn a flat ā¬500 a year ā ā¬20,000 after 20 years instead of ā¬26,533. The gap keeps widening: in the third decade, compounding earns more than in the first two combined.
Adding ā¬1,200 at the end of every year (ā¬100 a month) to the same starting amount gives ā¬66,212 after 20 years, for ā¬34,000 actually paid in.
The rule of 72
To estimate how long it takes to double your money, divide 72 by the annual rate: at 6% about 12 years, at 4% about 18 years, at 8% about 9 years. It is a mental shortcut and is most accurate for rates between 4% and 10%.
Things to keep in mind
- Real vs nominal returns: if inflation runs at 2% and your savings earn 5%, your purchasing power grows by roughly 3% a year. Run the calculator with the rate minus inflation to see the result in today's money.
- Rates are not guaranteed: a savings account rate can change, and stock market returns vary widely from year to year. A constant rate is a simplification for planning.
- Fees and taxes compound too: a 1% annual fee on a 6% return reduces your gain over 30 years by about 30%.
- Compounding frequency: this calculator compounds once a year. Monthly compounding at the same nominal rate gives a slightly higher result (5% compounded monthly ā 5.12% a year).
Compound interest works against you on debt as well: unpaid credit card balances grow on the same principle. See the loan payment calculator for the borrowing side.
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original amount, so it grows by the same sum every year. Compound interest is calculated on the balance including past interest, so growth accelerates over time.
When are the yearly contributions added?
At the end of each year, after that year's interest. If you save monthly, enter twelve times your monthly amount; the result will be slightly conservative.
What rate should I use?
Use the rate your savings product pays, or a cautious long-term average for investments. Subtract expected inflation if you want the result in today's money.