Compound Interest Formula Explained
Every calculator on this site runs on some version of the compound interest formula. This page walks through each variant, where it comes from, and which of our tools already computes it for you.
The Basic Compound Interest Formula
A = P(1 + r/n)nt
Where A is the ending balance, P is the starting principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. A $5,000 deposit at 4.50% APY, compounded monthly, for 10 years grows to $7,834.96.
The Formula With Regular Contributions
Most savers add money regularly, not just once. Adding a periodic contribution turns the formula into a future-value-of-annuity calculation layered on top of the basic one -- the principal grows on its own while each new contribution starts earning interest from the moment it's added. This is exactly what the Savings Interest Calculator computes: enter your deposit, monthly contribution, rate, and compounding frequency, and it runs this version of the formula for you.
Continuous Compounding
A = Pert
This is the theoretical limit of compounding frequency -- as n approaches infinity, the formula simplifies to this version using Euler's number (e ≈ 2.71828). On the same $5,000 at 4.50% for 10 years, continuous compounding produces $7,841.56, just $6.60 more than monthly compounding. In practice, no savings account compounds continuously; this version mostly matters for academic and theoretical finance, not real bank accounts.
Solving for a Missing Variable
The formula also works in reverse. Say a $8,000 deposit grew to $10,500 after 6 years with annual compounding, and you want to know what rate it earned. Rearranging the formula to solve for r:
r = (A/P)1/t − 1
Plugging in the numbers: r = (10,500/8,000)1/6 − 1 ≈ 4.6365%. This kind of reverse calculation is useful for checking an account's actual historical return, or comparing an old CD or account statement against what you were told the rate would be.
Which Formula Matches Which Calculator
You don't need to do this math by hand. Each formula variant on this page maps to a specific tool:
- Basic formula, no contributions → CD Calculator
- Formula with regular contributions → Savings Interest Calculator
- Converting between a nominal rate and APY → APY Calculator
Frequently Asked Questions
What does each letter in the compound interest formula mean?
A is the ending balance, P is the starting principal, r is the annual rate as a decimal, n is how many times per year interest compounds, and t is the number of years.
Do real bank accounts use continuous compounding?
No. Real accounts compound daily, monthly, quarterly, or annually. Continuous compounding is a theoretical upper limit used mostly in academic finance, and the practical difference versus daily or monthly compounding is small.
How do I find the rate an account actually earned?
Rearrange the formula to solve for r: r = (A/P)^(1/t) - 1, using your starting balance, ending balance, and the number of years between them.
Why does my bank's calculator give a slightly different number than this formula?
Small differences usually come from the exact compounding frequency used, rounding at each period, or fees not reflected in the formula itself. See How Compounding Frequency Works for more on this.
Sources
- Continuous compounding as the theoretical limit of compounding frequency — CalculateCompoundInterest.org
Cedrick Reese
Savings Interest Calculator was created by Cedrick Reese, a retired veteran and web developer who enjoys building free, user-friendly online tools that simplify everyday tasks. His journey began in the early 2000s with affiliate marketing and niche site development, which grew into a passion for creating practical digital utilities and calculators. After retiring, he earned a Computer Systems Technician certificate from UEI College, completed Electro-Mechanical Technologies at Tulsa Welding School, and finished the Carpentry program at Florida State College at Jacksonville. Today he combines his technical background and craftsmanship by building furniture using traditional woodworking methods, gardening, and developing helpful online tools for users worldwide.