Compound Interest Calculator
See exactly how your savings will grow over time with compound interest and optional monthly contributions. Enter your starting principal, your monthly addition, your expected annual return, and how many years you plan to stay invested. The calculator shows future value, total contributions, interest earned, and your money's growth multiple.
Quick answer
Future value = P(1 + r/n)^(nt) + PMT × [((1+r/n)^(nt) − 1) / (r/n)]. Rule of 72: money doubles in roughly 72 / rate years.
Compound Interest Calculator
How compounding works
Compound interest is interest paid on interest. In the first year, you earn your rate on
the principal. In the second year, you earn it on principal + year-one interest. By year
twenty, the interest-on-interest has become most of your return. The core formula is
A = P(1 + r/n)^(nt) — final amount equals principal times one-plus-rate to
the power of compounding-periods-times-years.
When you add monthly contributions (an annuity), the math gets an extra term. Each month's contribution compounds for a different number of remaining months, and the total is summed via the annuity formula. The calculator combines both a lump-sum compound formula and an annuity formula to cover the typical "start with X, add Y per month" scenario.
When to use it
Use compound interest projections whenever you're making a long-term savings decision: a 401(k) contribution rate, a Roth IRA goal, an emergency fund target, or a down-payment timeline. The classic example: $200/month invested from age 25 to 65 at 7% becomes about $525,000. Starting the same plan at 35 instead — just ten years later — ends with about $245,000. The first decade of contributions is worth more than the last two combined because of compounding.
This calculator is also useful for testing assumptions. What if the rate is 5% instead of 7%? Run both. What if you can only contribute $100/month for the first five years? Run two phases and add them. Fiddling with inputs is how you build intuition for the numbers.
Common mistakes
- Using nominal returns instead of real. The stock market averages ~10% nominal but only ~7% after inflation. For a plan spanning decades, use real returns.
- Assuming the return is guaranteed. Markets are volatile. Your actual 20-year return could be 5% or 11% — the average is the long-run expectation, not a promise for any given period.
- Ignoring fees. A 1% expense ratio on an index fund eats about 1% per year — small-sounding but massive over decades. A 1% fee on a 40-year portfolio cuts the final balance by roughly 25%.
- Confusing simple and compound interest. A savings account paying "5% APR simple" pays you 5% on the original principal every year. Compound interest grows much faster over time.
Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt). A is the final amount, P the principal, r the annual rate, n the compounding periods per year, and t the years.
How does compounding frequency affect growth?
More frequent compounding produces slightly more growth, but the effect is small. $10,000 at 7% for 20 years: annually = $38,697, monthly = $40,387, daily = $40,540.
What is the rule of 72?
A shortcut: years to double ≈ 72 / annual rate. At 6% money doubles in 12 years. At 9%, in 8 years.
Is 7% a realistic return?
7% is close to the long-run real return of the US stock market. Nominal returns are ~10%, but inflation eats ~3%.