Compound Interest Calculator
What a deposit or investment grows to with compound interest, compounded yearly, quarterly, monthly or daily, with optional monthly additions. Any currency.
10,000 at 7% a year compounded monthly grows to $20,096.61 in 10 years ($10,096.61 of interest). Adding 200 a month as well, it grows to $54,713.58, of which $20,713.58 is interest.
The words on this page, explained simply
New to this? Here is what each term means, in plain English.
- Compound interest
- Interest earned on earlier interest as well as on the original amount, so growth snowballs over time.
- Compounding frequency
- How often interest is added to the balance: yearly, quarterly, monthly or daily.
- Effective annual rate
- What a nominal rate is worth after compounding: 7% compounded monthly is about 7.23% a year.
- Rule of 72
- Years to double money ≈ 72 ÷ yearly rate.
- Simple interest
- Interest on the original amount only: principal × rate × time.
Compound interest is interest on interest: each period's interest is added to the balance and earns interest itself. Over long periods it is the difference between money that grows in a straight line and money that snowballs.
Choose how often interest is added (banks often compound monthly or daily, many bonds twice a year) and whether you add money each month.
The compound interest formula
A = P × (1 + r/n)n × t, where P is the starting amount, r the yearly rate as a decimal, n the number of times interest is added each year and t the years. 10,000 at 7% compounded monthly for 10 years: 10,000 × (1 + 0.07/12)120 = $20,096.61.
With monthly additions the calculator steps month by month: the balance grows by (1 + r/n)n/12, the month's share of the year's compounding, and each addition lands at the month's end.
The effective annual rate, (1 + r/n)n − 1, is what the nominal rate is really worth after compounding: 7% compounded monthly is 7.229% a year.
How compounding frequency changes the result
| 10,000 at 7% for 10 years | Final balance | Interest |
|---|---|---|
| Yearly | $19,671.51 | $9,671.51 |
| Quarterly | $20,015.97 | $10,015.97 |
| Monthly | $20,096.61 | $10,096.61 |
| Daily | $20,136.18 | $10,136.18 |
| Simple interest (no compounding) | $17,000.00 | $7,000.00 |
More frequent compounding helps, but far less than a higher rate or a longer time.
Key takeaways
- A = P(1 + r/n)^(nt).
- More frequent compounding earns a little more; time and rate matter most.
- Effective annual rate = (1 + r/n)^n − 1.
- Rule of 72: money doubles in about 72 ÷ rate years.
Frequently asked questions
How do you calculate compound interest?
Multiply the starting amount by (1 + rate ÷ periods per year) raised to the power of (periods per year × years), then subtract the starting amount for the interest alone.
What is the difference between simple and compound interest?
Simple interest is paid on the original amount only; compound interest is also paid on the interest already earned. 10,000 at 7% for 10 years earns 7,000 simple interest but 10,097 compounded monthly.
How long does it take to double money?
Roughly 72 divided by the yearly rate: about 10 years at 7%, 9 at 8%. The exact time is ln 2 ÷ ln(1 + rate); see the rule of 72 calculator.
Is daily compounding better than monthly?
Slightly. At 7%, daily compounding gives an effective 7.250% a year against 7.229% for monthly.