CalcKit
Compound Interest Calculator
Compound interest is interest earned on both the original amount and the interest already added to it. Each period, the interest joins the balance and earns interest itself, so savings grow faster and faster: interest on interest.
Enter the initial amount, the yearly rate, the number of years and how often the interest is compounded. An optional regular addition, per year, quarter, month, week or day, is added at the end of each compounding period.
The formula
Without additions:
Final value = Initial * (1 + r / n)^(n * t)
with r the yearly rate as a decimal (5% is 0.05), n the compounding periods per year (12 for monthly) and t the years.
Regular additions grow as a series of payments, each one compounding from the period it is added:
Additions' value = a * ((1 + r / n)^(n * t) - 1) / (r / n)
where a is the addition per compounding period. The calculator works it out in the background from your addition: $100 a month is $1,200 a year, which with monthly compounding is $100 per period, and with quarterly compounding $300. The final value is the sum of the two parts.
It also shows how much of the final value you put in (the contribution) and how much is interest.
Example
$1,000 at 5% a year for 10 years, compounded monthly, adding $100 a month:
- Final value: 17,175.24
- Contribution:
1,000 + 1,200 * 10 = 13,000.00 - Interest: 4,175.24
Without the additions, the $1,000 alone grows to 1,647.01, while simple interest would give $1,500.
Compounding frequency
More frequent compounding earns a little more, because interest starts earning interest sooner. $1,000 at 5% for 10 years grows to:
| Compounding | Final value |
|---|---|
| Yearly | 1,628.89 |
| Quarterly | 1,643.62 |
| Monthly | 1,647.01 |
| Daily | 1,648.66 |
The time and the rate matter far more than the frequency.
Frequently asked questions
How long does it take to double my money?
Roughly 72 divided by the yearly rate in percent, the rule of 72. At 6%, about 12 years; at 8%, about 9.
What is the difference between APR and APY?
The APR is the yearly rate before compounding, and the APY (or AER) is what you actually earn in a year once compounding is counted. 5% compounded monthly is an APY of 5.12%.