Compound Interest Calculator
See how your savings grow over time with compounding.
What is the Compound Interest Calculator?
Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan. Thought of as "interest on interest," compound interest will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.
The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest. Thus, an amount of $10,000 compounded at 10% annually will yield less than if it were compounded semi-annually or quarterly.
Practical Examples & Reference Guide
Here is a practical comparison of how an initial investment of $10,000 grows over various horizons at an 8% annual return, comparing Simple Interest vs. Compound Interest (compounded annually):
| Investment Period | Simple Interest Total | Compound Interest Total | Wealth Difference |
|---|---|---|---|
| 5 Years | $14,000 | $14,693 | +$693 |
| 10 Years | $18,000 | $21,589 | +$3,589 |
| 20 Years | $26,000 | $46,610 | +$20,610 |
| 30 Years | $34,000 | $100,627 | +$66,627 |
As you can see, the compounding effect accelerates dramatically over longer time horizons.
In-Depth Technical Guide
The Mathematical Formula for Compound Interest
To calculate compound interest, you use the standard compounding formula:
$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit)
- r = the annual interest rate (decimal format, e.g., 0.05 for 5%)
- n = the number of times that interest is compounded per unit $t$ (usually per year)
- t = the time the money is invested or borrowed for (usually in years)
How Compounding Frequency Matters
The compounding frequency is the number of times the interest is calculated and added to the principal balance per year. Standard intervals include:
- Annual (n = 1): Interest is calculated once a year.
- Semi-Annual (n = 2): Interest is calculated twice a year (every 6 months).
- Quarterly (n = 4): Interest is calculated four times a year (every 3 months).
- Monthly (n = 12): Interest is calculated monthly.
- Daily (n = 365): Interest is calculated every single day.
For example, if you invest $10,000 at a 6% interest rate for 5 years:
- Compounded Annually: $10,000 * (1 + 0.06/1)^5 = $13,382.26
- Compounded Monthly: $10,000 * (1 + 0.06/12)^60 = $13,488.50
- Compounded Daily: $10,000 * (1 + 0.06/365)^1825 = $13,498.26