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Investing & Retirement
Compound Interest Calculator — Future Value with Monthly Contributions
How a starting balance and steady deposits snowball into real money
Compound interest is the engine behind every 401(k), Roth IRA, brokerage account and high-yield savings account in America. It's the reason financial planners say time in the market beats timing the market — because compounding is interest earning interest, and the longer it runs, the steeper the curve gets.
The idea is simple: each period your money earns a return, and that return gets added to the balance. Next period you earn a return on the bigger balance. Repeat for 20 or 30 years and the growth becomes dramatic — most of an ending balance is often interest, not the dollars you actually deposited.
There are two pieces to the math. First, your starting principal grows on its own: FV = P × (1 + i)^n, where i is the rate per period and n is the number of periods. Second, your recurring contributions form an annuity, and each deposit compounds for the time it stays invested: FV = PMT × [ ((1 + i)^n − 1) ÷ i ]. Add the two together for your total future value.
Worked example. Start with $10,000, add $200 a month, earn 7% a year, and let it run 10 years, compounded monthly. The monthly rate is 0.07 ÷ 12 = 0.0058333, over n = 120 months.
- Principal grows to 10,000 × (1.0058333)^120 = $20,096.61
- Contributions grow to 200 × [((1.0058333)^120 − 1) ÷ 0.0058333] = $34,616.97
- Future value ≈ $54,713.58
You put in just $34,000 ($10,000 + $24,000 of deposits), so roughly $20,714 of that ending balance is pure compound interest.
The most common mistake is using the annual rate as if it were the monthly rate. If you deposit monthly, you must divide the annual rate by 12 and count months, not years. Plugging 7% straight into a monthly formula massively overstates the result. The second trap is forgetting that this calculator shows nominal dollars — it does not subtract inflation, taxes, or account fees, all of which shrink real-world returns. Treat the output as an estimate of growth, not a guarantee.
Use the calculator below to size up a savings goal, compare contribution amounts, or just watch how a few extra dollars a month change the finish line.
Calculator
Fill in the fields and click "Calculate" for instant results.
📰 Formula
• Rate per period: i = annual rate ÷ periods per year • Periods: n = years × periods per year • Future value of principal: FV₁ = P × (1 + i)ⁿ • Future value of contributions: FV₂ = PMT × [((1 + i)ⁿ − 1) ÷ i] • Future value = FV₁ + FV₂ • Total contributions = P + (PMT × n) • Interest earned = Future value − Total contributions
📰 Formula
• Rate per period: i = annual rate ÷ periods per year • Periods: n = years × periods per year • Future value of principal: FV₁ = P × (1 + i)ⁿ • Future value of contributions: FV₂ = PMT × [((1 + i)ⁿ − 1) ÷ i] • Future value = FV₁ + FV₂ • Total contributions = P + (PMT × n) • Interest earned = Future value − Total contributions
🧪 Worked examples
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Example 2
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Example 3
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Example 4
⚠️ Common mistakes
- Using the annual rate in a monthly formula instead of dividing by 12.
- Counting years as the number of periods when compounding monthly (use months).
- Mixing the contribution frequency with a different compounding frequency.
- Reading the result as guaranteed take-home money — it ignores inflation, taxes, and fees.
💡 Tips
- Match your deposit frequency to the compounding frequency for the cleanest estimate.
- Starting earlier usually beats contributing more — extra years compound the hardest.
- Use a realistic long-run rate (often 5–8% for diversified stocks) rather than a best-case year.
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❓ Frequently asked questions
What is the compound interest formula with monthly contributions?
Future value = P × (1 + i)ⁿ + PMT × [((1 + i)ⁿ − 1) ÷ i], where i is the rate per period (annual rate ÷ 12) and n is the number of months. The first term grows your starting balance; the second grows your deposits.
How do I calculate compound interest on a savings account?
Take your balance, multiply by (1 + i)ⁿ. For a $10,000 balance at 5% compounded monthly for 3 years: i = 0.05 ÷ 12 and n = 36, so 10,000 × (1.004167)^36 ≈ $11,614 — about $1,614 of interest.
What's the difference between simple and compound interest?
Simple interest is paid only on your original principal each period. Compound interest is paid on the principal plus all the interest already earned, so the balance grows faster and the gap widens over time.
Does compounding monthly earn more than annually?
Yes, slightly, for the same stated rate. More frequent compounding means interest is added and starts earning sooner. The effect is small for one year but adds up over decades.
How much will $10,000 grow in 20 years?
At 7% compounded monthly with no extra deposits, $10,000 becomes about $40,387 in 20 years. Add $200 a month and it grows to roughly $144,573.
What interest rate should I use for investments?
For a diversified stock portfolio, many planners model 5–8% a year as a long-run average. Savings accounts and CDs are usually lower. Use a conservative figure rather than a single great year.
Does this calculator account for taxes and inflation?
No. It shows nominal growth before taxes, fees, and inflation. Real spending power will be lower — inflation alone often shaves a few percentage points off the rate each year.
What is the Rule of 72?
A quick shortcut: divide 72 by your annual rate to estimate the years it takes money to double. At 8%, that's about 72 ÷ 8 = 9 years. It's an approximation, not the exact compound formula.
Should I contribute at the start or end of each month?
Depositing at the start of each period earns a little extra interest because the money compounds one period longer. This calculator uses end-of-period (ordinary annuity) deposits, the standard conservative assumption.