Compound Interest
Compound interest is what happens when your interest starts earning interest. Instead of growth coming only from your original principal, the balance compounds as each period’s interest becomes part of the new base. Over long horizons, small differences in rate, contribution habit, and compounding frequency can produce surprisingly different outcomes.
Use this compound interest calculator to estimate an ending balance for savings, investing, or even debt that grows over time. You can include regular contributions, choose whether deposits happen at the end or beginning of each period, and compare discrete compounding (daily/monthly/etc.) with continuous compounding.
Want a quick contrast? You can compare with simple interest, or if you’re modeling a bank product you may prefer the CD interest calculator. Explore more tools on our hub: Explore more finance calculators.
Calculator
- Estimated ending balance (future value) with compounding
- Total contributions vs. total interest earned
- Effective annual rate (EAR), including continuous compounding
- Year-by-year breakdown table and a growth trend visualization
- Optional inflation-adjusted value in today’s dollars
Results
How compound interest works
Compound interest grows your balance by applying interest repeatedly over time. With discrete compounding, your annual rate (APR) is split into periodic rate i = r/n, and your total number of periods is N = n × t, where:
- P = initial principal
- PMT = regular contribution per compounding period (can be 0)
- r = annual rate (APR as a decimal)
- n = compounding periods per year (12 monthly, 365 daily, etc.)
- t = time in years
Discrete compounding (no contributions) uses:
FV = P × (1 + r/n)^(n×t)
With regular contributions (end of period / ordinary annuity), the future value is:
FV = P×(1+i)^N + PMT × [((1+i)^N − 1) / i]
If you deposit at the beginning of each period (annuity due), the contribution term is multiplied by (1+i). If you’re modeling debt with interest-only behavior, see interest-only payment scenarios.
Continuous compounding is the theoretical limit where compounding happens “all the time”:
FV = P × e^(r×t)
This page also reports the effective annual rate (EAR). For discrete compounding: EAR = (1 + r/n)^n − 1. For continuous compounding: EAR = e^r − 1.
Use cases
- Project a savings goal (emergency fund, down payment, or a big purchase) with monthly deposits.
- Estimate long-term investing growth, where compounding plus steady contributions do most of the work.
- Compare how daily vs monthly vs annual compounding changes the final balance at the same APR.
- Model balance growth on interest-bearing debt if payments are too small to reduce principal.
- Plan retirement contributions and cross-check assumptions using related tools like the 401(k) loan cost implications calculator.
Examples (worked)
Example 1: Lump sum only (no contributions)
Inputs: P = $10,000, PMT = $0, APR = 6%, Compounding = Monthly (n=12), Time = 10 years.
i = r/n = 0.06/12 = 0.0050 N = n×t = 12×10 = 120 FV = 10,000 × (1.0050)^120 ≈ 10,000 × 1.8194 ≈ $18,194
Takeaway: even without deposits, compounding grows the base because interest keeps joining the balance.
Example 2: Regular monthly deposits (end of period)
Inputs: P = $5,000, PMT = $200 (monthly), APR = 7%, n=12, Time = 20 years, Timing = End of period.
i = 0.07/12 ≈ 0.005833 N = 12×20 = 240 FV = 5,000×(1+i)^N + 200×[((1+i)^N − 1)/i] (1+i)^N ≈ (1.005833)^240 ≈ 4.037 FV ≈ 5,000×4.037 + 200×[(4.037−1)/0.005833] FV ≈ 20,185 + 200×520.6 ≈ 20,185 + 104,120 ≈ $124,305
Takeaway: contributions plus compounding can dominate long horizons—most of the ending balance often comes from the repeated growth on earlier deposits.
Example 3: Continuous compounding (principal only)
Inputs: P = $20,000, PMT = $0, APR = 5%, Compounding = Continuous, Time = 15 years.
FV = 20,000 × e^(0.05×15) = 20,000 × e^0.75 e^0.75 ≈ 2.1170 FV ≈ 20,000 × 2.1170 ≈ $42,340
Takeaway: continuous compounding is slightly higher than discrete compounding at the same APR. If you also want deposits, choose a discrete frequency (monthly/quarterly/etc.) so contributions are applied correctly.
Common Mistakes
- Mixing up APR and EAR (the effective rate depends on compounding frequency).
- Entering a monthly contribution while selecting quarterly or annual compounding (PMT is per compounding period).
- Ignoring contribution timing—beginning-of-period deposits (annuity due) grow more than end-of-period deposits.
- Assuming daily compounding dramatically changes results; it’s usually a small difference compared to your rate and time horizon.
- Forgetting inflation: a higher nominal future value may still buy less if inflation is high over many years.
Quick Tips
- Start earlier: time is the biggest multiplier in compounding.
- Increase contributions gradually (even small annual bumps can matter over decades).
- Check your compounding frequency and make PMT match it (monthly with monthly is the most common).
- Use inflation-adjusted mode for long-term goals to keep expectations realistic.
- Stress-test with a lower rate and longer time; conservative planning is usually more resilient.
Accuracy & Privacy
Accuracy & Method: All calculations run locally in your browser using standard compound interest formulas (and an EAR conversion based on your compounding choice). No server calls are required.
Privacy-first: The numbers you enter stay on your device and are not transmitted.
Rounding: Currency outputs are rounded to 2 decimals; intermediate rate values may display with up to 4 decimals for transparency.
Sources & References (plain-text):
- Investor.gov educational materials on compounding and saving
- SEC investor resources for long-term planning concepts
- Major bank and brokerage educational pages on APY/EAR and compounding frequency
- Standard time value of money (TVM) and annuity formulas used in finance textbooks