Know where you started, where you ended up and how long it took? This calculator works backwards to the annual interest rate — for simple interest or for compound interest at any frequency — and shows the effective annual rate.
Interest Rate Calculator
Find the annual interest rate that turns a starting amount into a final amount.
Results are estimates for educational purposes and are not financial advice. Actual returns depend on your provider's terms, fees and taxes.
Formulas used
Compound interest — rearranging A = P(1 + r/n)nt for r:
r = n × [ (A ÷ P)1 ÷ (n × t) − 1 ]
Simple interest — rearranging A = P(1 + R × T ÷ 100):
R = ( A ÷ P − 1 ) ÷ T × 100
Effective annual rate (any method): (A ÷ P)1/t − 1. This is the compound annual growth rate (CAGR).
- P
- Starting amount.
- A
- Final amount (must be at least the starting amount).
- t
- Time in years.
- n
- Compounding periods per year.
How to use
- Enter the starting amount and the final amount.
- Enter the time between them.
- Choose the interest type: compound (with its frequency) or simple.
- Press Calculate to see the required rate.
Worked example
An investment grew from $10,000 to $15,000 in 6 years. What rate did it earn?
- Compounded monthly: r = 12 × [(15,000 ÷ 10,000)1/72 − 1] = 12 × (1.005647 − 1) = 6.7768%.
- Compounded annually (= CAGR): (1.5)1/6 − 1 = 6.9913%.
- Simple interest: (1.5 − 1) ÷ 6 × 100 = 8.3333%.
The same growth needs a lower nominal rate when compounding is more frequent, and a noticeably higher rate if no compounding happens at all.
Practical uses
- Finding the actual return earned on a past investment (CAGR).
- Working out the rate a deposit must pay to hit a savings goal.
- Checking the true interest rate implied by an informal loan (“borrow $1,000, repay $1,300 in two years”).
- Comparing offers that state results (“double your money in 10 years”) rather than rates.
Assumptions and limitations
- One amount at the start and one at the end — no deposits or withdrawals in between. With regular deposits the true return needs an internal rate of return (IRR) calculation.
- The rate is assumed constant over the whole period. For investments with ups and downs, the result is the smoothed average.
- The final amount must not be lower than the starting amount.
Frequently asked questions
What is CAGR?
Compound annual growth rate — the constant yearly rate that would take you from the starting to the final value. It equals the result with annual compounding here.
Why are the monthly and annual answers different?
They describe the same growth in different ways. 6.7768% compounded monthly and 6.9913% compounded annually both turn $10,000 into $15,000 in 6 years.
Can I find the rate for a loan with monthly payments?
Not with this tool. Loans with regular repayments need an amortisation (annuity) rate calculation.