The compound interest formula is one of the most important equations in personal finance. Once you understand it, you can calculate exactly how any investment will grow — and make better financial decisions for the rest of your life. Let's break it down into plain English.
The Core Formula
A = P × (1 + r/n)^(n × t)- A = Final amount (the future value of your investment)
- P = Principal (your initial investment or starting balance)
- r = Annual interest rate as a decimal (e.g., 8% = 0.08)
- n = Number of compounding periods per year (daily=365, monthly=12, quarterly=4, annually=1)
- t = Time in years
Understanding Each Variable
P — Principal
The principal is the starting seed money. The larger your principal, the more interest each compounding period generates. Even small differences in starting principal have large effects over time. $10,000 vs $15,000 at 8% for 30 years is $109,357 vs $164,036 — a $54,679 difference from just $5,000 more at the start.
r — Annual Interest Rate
Always convert percentage to decimal before using in the formula: 8% → 0.08. This is the most impactful variable after time. Even a 1% difference in rate produces dramatically different outcomes over long periods.
n — Compounding Frequency
This determines how many times per year interest is calculated. The formula divides the rate by n (r/n) to get the per-period rate, and multiplies time by n (n×t) to get total periods. Monthly compounding (n=12) gives slightly more than annual (n=1) but the difference is modest.
t — Time in Years
Time is the most powerful variable. Due to the exponential nature of the formula, small increases in t produce enormous increases in A — especially at higher interest rates. The exponent n×t grows rapidly, driving the final value up exponentially.
The Extended Formula: With Monthly Contributions
A = P(1+r/n)^(nt) + PMT × [((1+r/n)^(nt) − 1) / (r/n)]- PMT = Periodic (monthly) contribution amount
- The second term calculates the future value of an annuity (series of payments)
- All other variables are the same as the basic formula
This is the formula our compound interest calculator uses. It gives you the most complete and accurate projection when you plan to make regular contributions.
Worked Examples
Example 1: $5,000 at 6% compounded annually for 10 years
A = 5,000 × (1 + 0.06/1)^(1×10) = 5,000 × (1.06)^10 = 5,000 × 1.7908 = $8,954
Example 2: $5,000 at 6% compounded monthly for 10 years
A = 5,000 × (1 + 0.06/12)^(12×10) = 5,000 × (1.005)^120 = 5,000 × 1.8194 = $9,097
Monthly compounding added $143 over 10 years — the power of more frequent compounding.
Bonus: Continuous Compounding
When compounding happens infinitely often (theoretically), the formula simplifies using Euler's number (e ≈ 2.718):
A = P × e^(r × t)- This is the theoretical maximum of compounding
- Example: $5,000 at 6% for 10 years: A = 5,000 × e^(0.6) = 5,000 × 1.8221 = $9,111
- Only $14 more than daily compounding — showing the practical limit of frequency
Apply the Formula to Your Situation
Use our free calculator — just enter your numbers and it handles all the formula calculations instantly.
Try Calculator FreeFrequently Asked Questions
A = P(1 + r/n)^(nt). Where A=final amount, P=principal, r=annual rate (decimal), n=compounding periods/year, t=years. With contributions: add PMT×[((1+r/n)^nt-1)/(r/n)].
Divide by 100: 8% → 0.08, 5.5% → 0.055, 12% → 0.12. This decimal form is what goes into the formula for r.
Continuous compounding: A = Pe^(rt). It's the theoretical maximum — compounding every instant. The formula uses Euler's number (e≈2.718). In practice, daily compounding gets very close to continuous.
Yes: =FV(rate/n, n*years, -monthly_contribution, -principal) gives the same result as the extended formula. Example: =FV(0.08/12, 12*20, -200, -10000).