Practical guide
How to Calculate Compound Interest
Understand compounding growth with principal, rate, time, and contributions.
Quick Answer
Step-by-Step Method
- Identify principal (P), annual rate (r), compounding frequency (n), and time in years (t).
- Convert the annual rate to decimal form (divide percent by 100).
- Apply A = P(1 + r/n)^(nt) to find the future value.
- Subtract principal from A to see total interest earned.
Worked Example
$5,000 at 6% APR compounded monthly for 10 years: r = 0.06, n = 12, t = 10. A ≈ $9,096. Total interest ≈ $4,096.
Detailed Explanation
Compounding frequency changes the outcome even when the nominal rate is identical, because interest starts earning interest sooner. At 6% nominal, annual compounding yields exactly 6% over a year while monthly compounding yields about 6.17% and daily slightly more. That gap is what the distinction between APR and APY captures: APR states the nominal rate, APY states what you actually receive once compounding is accounted for. When comparing savings accounts, compare APY — comparing an APR against an APY is not a like-for-like comparison.
The Rule of 72 gives a fast mental estimate of doubling time: divide 72 by the annual percentage rate. At 6%, money doubles in roughly 12 years; at 9%, in about 8. It is an approximation that works best between roughly 4% and 12%, but it is accurate enough to sanity-check a projection in your head and to make the cost of a few percentage points intuitive in a way that a formula does not.
The same mechanism runs in both directions, and this is the part worth internalising. Compounding builds savings and it builds debt, with credit card balances the clearest example — interest compounding monthly on a balance you are not clearing produces the same exponential curve, pointed the wrong way. Time is the dominant variable on both sides, which is why starting to save early beats saving more later, and why clearing high-interest debt early beats almost any investment return you could earn instead.
Use the Calculator
Run your real values in the interactive tool and review assumptions before taking action.
Open related calculatorFAQ
What is the difference between simple and compound interest?
Simple interest applies only to the original principal. Compound interest applies to principal plus accumulated interest.
How often should savings compound?
More frequent compounding yields slightly higher returns. Daily or monthly is typical for savings accounts.
Does inflation affect compound growth?
Yes. Real return ≈ nominal return minus inflation. Factor inflation when planning long-term goals.