Interest Rate Calculator
Solve for the annual interest rate given PV, FV, time, and compounding.
| # | Date | Start | Interest | End |
|---|---|---|---|---|
| Run a calculation to see the schedule. | ||||
Use this Interest Rate Calculator to find the annual interest rate needed for a starting amount to grow to a specified future value over a selected period. The calculator accounts for annual, semiannual, quarterly, monthly, daily, or continuous compounding.
Important: The result is a mathematical compound-growth rate. It is not necessarily the same as a lender’s official APR, an advertised savings APY, or a future investment return.
Interest Rate Calculation
For regular compound interest:
FV = PV × (1 + r ÷ n)n × t
Solving this formula for the nominal annual interest rate gives:
r = n × [(FV ÷ PV)1 ÷ (n × t) − 1]
Where:
- PV = present value or starting amount
- FV = future value or ending amount
- r = nominal annual interest rate
- n = compounding periods per year
- t = time in years
The periodic interest rate is:
Periodic rate = (FV ÷ PV)1 ÷ total periods − 1
The effective annual rate (EAR) is:
EAR = (1 + r ÷ n)n − 1
Continuous Compounding
If continuous compounding is selected:
FV = PV × er × t
Therefore:
r = ln(FV ÷ PV) ÷ t
Worked Example
Suppose you want $10,000 to grow to $15,000 over 5 years with monthly compounding.
Here:
- PV = $10,000
- FV = $15,000
- t = 5 years
- n = 12
Using the rate formula:
r = 12 × [($15,000 ÷ $10,000)1 ÷ 60 − 1]
The required nominal annual rate is approximately:
8.14% per year
The corresponding effective annual rate is approximately:
8.45% per year
This means that, under the calculator’s assumptions, monthly compounding at a nominal annual rate of about 8.14% would grow $10,000 to approximately $15,000 over five years.
Important Notes
- The calculator assumes one starting value and one ending value with no additional deposits or withdrawals.
- The calculated rate is assumed to remain constant throughout the selected period.
- Compounding frequency affects the nominal annual rate and periodic rate.
- EAR reflects the annual effect of compounding. For deposit accounts, APY is also used to express annual yield including compounding.
- This calculator does not calculate the official APR of an amortizing loan with monthly payments and fees.
- Loan APR can include finance charges and other costs that are not represented by this compound-growth formula.
- For investments, the calculated rate is an implied or required growth rate, not a prediction or guaranteed return.
- Taxes, inflation, fees, changing rates, investment volatility, and additional cash flows are not included.