The Magic of Compound Interest
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
As famously noted by the Federal Reserve, consistent saving combined with the power of compounding is the most reliable path to long-term wealth accumulation for the average individual.
The Mathematical Formula
The standard formula for compound interest is:
A = P(1 + r/n)nt
- A: The future value of the investment/loan, including interest.
- P: The principal investment amount (the initial deposit).
- r: The annual interest rate (decimal).
- n: The number of times that interest is compounded per unit t.
- t: The time the money is invested or borrowed for.
Compounding Frequency Matters
The frequency at which interest is calculated and added back to the principal significantly impacts the final amount. The more frequent the compounding, the higher the final balance.
| Frequency | Compounding Periods (n) |
|---|---|
| Daily | 365 |
| Monthly | 12 |
| Quarterly | 4 |
| Annually | 1 |
Why Use This Calculator?
While the math seems simple, manual calculation becomes extremely tedious when dealing with monthly contributions and different compounding periods. Our engine, based on principles outlined by NIST Math Standards, ensures that every cent is accounted for precisely.
Expert Tip: The Rule of 72
To find out how many years it will take for your money to double with compound interest, divide 72 by your annual interest rate. For example, at a 6% interest rate, your money will double in approximately 12 years (72 / 6 = 12).