Interest Rate Calculator — Find the Rate You Were Charged
Calculate the effective interest rate from a starting principal and final amount. Supports compound and simple interest across any time period. Shows the algebraic formula used to isolate r.
Interest Rate Calculator
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Formula Applied
r = n × [(A/P)^(1/nt) − 1]
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EAR accounts for compounding — it is the true annual rate
Total Interest
$4,500
Total Growth
45.00%
The Formula
This formula algebraically isolates the nominal annual interest rate r from the compound interest equation A = P(1 + r/n)^(nt). It is the reverse of calculating a future value — given that you know the outcome, what rate produced it? This is frequently needed when evaluating actual investment performance or understanding the true cost of a loan.
Variable Definitions
Nominal Annual Rate
The interest rate per year, before accounting for compounding. This is the rate stated on most financial products — the APR or nominal yield. To convert to an effective rate, use the EAR formula: (1 + r/n)^n − 1.
Final Amount
The total amount after growth or the total repaid on a loan. Must be greater than P to calculate a positive interest rate.
Principal
The starting amount — the original investment or original loan balance. The rate calculation is very sensitive to P, so accuracy matters.
Compounding Frequency
How many times per year interest compounds (12 = monthly, 365 = daily, 1 = annually). Selecting the wrong n produces a significantly different result.
Time (years)
The number of years the money was invested or the loan was held. Entered as years, months, or days — this calculator automatically converts non-year inputs.
Effective Annual Rate
The real annual rate after accounting for compounding: EAR = (1 + r/n)^n − 1. This is the true rate for comparing products with different compounding frequencies.
How to Use This Calculator
- 1
Enter the starting principal — the original amount of money.
- 2
Enter the final amount — what the investment or loan grew/cost in total.
- 3
Enter the time period and select whether it's in years, months, or days.
- 4
Select the compounding frequency that matches the product (check your statement or loan agreement).
- 5
The calculator returns the nominal annual rate, effective annual rate, and the formula used.
- 6
Use the "Simple Interest" option when interest is not reinvested or compounded during the period.
Common Applications
- Determine the actual annual interest rate charged on a loan when you know the principal, total amount paid, and loan duration.
- Calculate the effective annual rate earned on an investment accounting for different compounding frequencies.
- Compare savings accounts and CDs with different nominal rates and compounding schedules by calculating their true effective rates.
This calculator solves for the interest rate by reversing the compound interest formula, isolating rate r from the known principal P, final amount A, time t, and compounding frequency n
Understanding the Concept
This calculator solves the reverse problem: instead of "what will my investment be worth?", it answers "what rate was I charged or earned?" This is useful when a bank advertises a savings account yield but compounds daily — you want to know the effective rate. It's also useful for evaluating investments where you know what you paid and what you received. The Effective Annual Rate (EAR) is the correct metric for comparing two products with different compounding schedules. For example, a savings account quoting 4.89% compounded monthly has an EAR of 5.00%, while a CD quoting 4.89% compounded daily has an EAR of approximately 5.01% — the daily compounding produces a slightly higher effective return at the same nominal rate.
Frequently Asked Questions
Sources & References
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