Interest Rate Calculator

Calculate the implied interest rate from an initial amount, final amount, and time period.

Compound Interest

Annual Nominal Rate

8.4472%

Effective Annual Rate

8.4472%

Rate per Period

8.4472%

r = (FV/PV)^(1/5) − 1 = 8.4472% per period

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Interest Rate Calculator Formula & How It Works

Simple: r = (A/P − 1) / t | Compound: r = (A/P)^(1/t) − 1
  • Simple rate: r = (A − P) / (P × t)
  • Compound rate: r = (A/P)^(1/(n×t)) × n
  • A = Final amount
  • P = Initial principal

When you know the starting amount, ending amount, and time period, you can solve for the interest rate. The calculation differs for simple vs compound interest. This is useful for evaluating investments: if you put in $1,000 and received $1,300 after 3 years, what annual rate did you earn?

Interest Rate Calculator FAQs

How do I calculate the interest rate on a loan from its payments?

For a loan with known payment, amount, and term, the rate requires iterative calculation (Newton-Raphson). This calculator handles the iteration for you — enter loan amount, monthly payment, and term to find the implied APR.

How do I find the real (inflation-adjusted) interest rate?

Real Rate = (1 + Nominal Rate) / (1 + Inflation Rate) − 1, approximately: Nominal Rate − Inflation Rate. If your savings account pays 4% and inflation is 3%, your real return is ~1%.

What is a good rate of return on an investment?

Historical benchmarks: US stock market ~10%/year (nominal), ~7% real. Bonds: 3–5%. Savings accounts: 0.5–5% depending on rates. Real estate: 8–12% total return including appreciation. Adjust for your risk tolerance.

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