Compound Interest Rate Calculator
Enter your starting balance, ending balance, time period, and how often interest is compounded, and this calculator works out the annual interest rate. It handles eight compounding frequencies from annually to daily, plus continuous compounding, and shows both the nominal rate and the equivalent Annual Percentage Yield (APY). A year-by-year growth chart and worked steps let you see exactly how the math unfolds.
Formula
Worked example
A $10,000 deposit grows to $15,000 over 5 years compounded monthly. Growth factor = 15,000 / 10,000 = 1.5. Nominal rate r = 12 x (1.5^(1/60) - 1) = 12 x (1.006715... - 1) = 12 x 0.006715 = 8.058% per year. APY = (1 + 0.08058/12)^12 - 1 = 8.372%.
What is the compound interest rate formula?
Compound interest means interest earned in one period is added to the principal before the next period starts, so each period earns a little more. The standard formula rearranged to solve for the annual rate r is: r = n x ((FV / PV)^(1/(n x t)) - 1), where PV is the starting balance, FV is the ending balance, t is the time in years, and n is the number of compounding periods per year. For continuous compounding, where interest is credited every instant, the formula simplifies to r = ln(FV / PV) / t. Both forms give you the nominal annual rate. To compare rates that use different compounding schedules on equal footing, convert to the Annual Percentage Yield (APY): APY = (1 + r/n)^n - 1.
Nominal rate vs APY - why both matter
Banks and investment products often advertise the nominal rate, which is just the annual rate before accounting for the effect of compounding within the year. A 6% nominal rate compounded monthly is not the same as a 6% rate compounded annually. Monthly compounding means each of the 12 sub-periods earns 0.5%, and those earnings themselves earn interest, pushing the effective annual return to about 6.168%. The APY (also called EAR, effective annual rate) captures this exactly. When comparing a daily-compounding savings account against an annually-compounding bond, always compare APYs, not nominal rates. This calculator shows you both.
Compounding frequency and its impact
The more frequently interest compounds, the faster a balance grows for the same nominal rate. Moving from annual to monthly compounding on a $10,000 investment at 8% over 10 years increases the final balance from $21,589 to $22,196. Moving to daily compounding pushes it to $22,253. The marginal gain narrows as frequency increases, and continuous compounding (mathematical infinity of periods) is the upper bound. In practice, the difference between monthly and daily is small, while the difference between annual and monthly is meaningful over long horizons.
Common uses for this calculator
This tool is most useful when you know both the beginning and ending values of an investment and want to find the implied rate of return - for example, checking the effective rate on a savings bond, verifying what CAGR (compound annual growth rate) a mutual fund has delivered, or determining the rate charged on a lump-sum loan where you only know what you borrowed and what you repaid. The result is equivalent to the CAGR when no additional contributions are made during the period. For mortgages or loans with regular payments, use an amortization calculator instead, which accounts for the periodic payment structure.
Typical annual interest rates by account type
| Account / instrument | Typical rate range | Compounding |
|---|---|---|
| Traditional savings account | 0.01% - 0.5% | Daily or monthly |
| High-yield savings account | 4.5% - 5.5% | Daily |
| 1-year Certificate of Deposit | 4.5% - 5.5% | Daily or monthly |
| 5-year CD | 4.0% - 5.0% | Daily or monthly |
| Money market account | 4.0% - 5.5% | Daily |
| US 10-year Treasury note | 4.0% - 5.0% | Semi-annually |
| S&P 500 (historical avg, CAGR) | ~10% nominal | N/A (reinvested) |
| 30-year fixed mortgage | 6.5% - 7.5% | Monthly |
| Personal loan | 8% - 36% | Monthly |
Approximate nominal annual rates as of 2024-2025. Actual rates vary by provider and market conditions.
Frequently asked questions
What is the difference between nominal rate and APY?
The nominal rate is the stated annual rate before compounding within the year is factored in. APY (Annual Percentage Yield) reflects the actual return you earn after compounding is applied. For example, 6% compounded monthly has an APY of about 6.168%. Always compare APYs when evaluating products that compound at different frequencies.
How do I find the interest rate on an investment when I only know start and end values?
Enter your starting balance as PV, your ending balance as FV, and the length of the investment period. Select the compounding frequency that matches your account. The calculator applies the formula r = n x ((FV/PV)^(1/(n x t)) - 1) to give you the nominal annual rate and the APY.
What is the CAGR and is it the same as the compound interest rate?
CAGR stands for Compound Annual Growth Rate. When no contributions or withdrawals are made during the period, the CAGR is identical to the annual compound interest rate compounded once per year (n = 1). Many investment reports quote CAGR because it reduces multi-year performance to a single comparable annual figure.
How does continuous compounding differ from daily compounding?
Continuous compounding is a mathematical limit: interest is credited every instant rather than at discrete intervals. The formula switches from the power function to an exponential: FV = PV x e^(r x t). In practice, the difference between daily and continuous compounding is tiny. On a $10,000 deposit at 5% for 10 years, daily gives $16,486.65 and continuous gives $16,487.21, a difference of less than a dollar.
Can this calculator find the rate for a loan?
Yes, for simple lump-sum loans where you borrow a principal and repay a single larger amount. Enter the loan amount as PV and the total repayment amount as FV. For loans with regular monthly payments (like mortgages or car loans), you need an amortization calculator, because those use a different formula that accounts for the payment stream.
Why does the calculator require FV to be greater than PV?
A compound interest rate only makes sense when the ending balance exceeds the starting balance (positive growth). If FV equals PV the rate is 0%, and if FV is less than PV the rate would be negative, which indicates a loss rather than interest earned. For depreciation or loss scenarios, a separate rate-of-return calculator that handles negative rates is more appropriate.