What It Does
The Savings Interest Rate Calculator works backwards from what actually happened to your money. If you know how much you deposited, how much it grew to, and how long it took, this tool reveals the annual interest rate that produced that growth. It's the inverse of a compound-interest calculator — instead of projecting a balance, it solves for the rate.
How to Use It
Enter your initial deposit (the present value), the final balance (the future value), the number of years the money was invested, and how often interest compounds per year (monthly, quarterly, annually, etc.). The calculator returns the nominal annual rate, the effective annual yield (APY), and the total interest earned.
The Formula Explained
The growth of a deposit under compound interest is \( FV = PV \times (1 + r/n)^{n \cdot t} \). Rearranging to isolate the rate gives:
$$r = n \left[ \left( \frac{FV}{PV} \right)^{\frac{1}{n \cdot t}} - 1 \right]$$Here \(n\) is the number of compounding periods per year and \(t\) is the number of years. The result \(r\) is the nominal annual rate. The APY then restates that rate as a single effective annual figure: \( APY = (1 + r/n)^{n} - 1 \).
Worked Example
Suppose you deposited $10,000 and it grew to $12,000 over 5 years, compounding monthly (\(n = 12\)). Then \(n \cdot t = 60\) and \(FV/PV = 1.2\). So $$(1.2)^{1/60} \approx 1.0030441,$$ minus 1 gives \(0.0030441\), times 12 \(\approx 0.036529\) — a nominal rate of about 3.653%. The APY works out to roughly 3.716%, and total interest earned is $2,000.
FAQ
What's the difference between rate and APY? The nominal rate ignores compounding within the year; APY folds compounding in, so it's always slightly higher when interest compounds more than once a year.
Does this work for any currency? Yes — the math is currency-agnostic. Just use the same currency for deposit and final balance.
What if I made extra contributions? This calculator assumes a single lump-sum deposit with no additions or withdrawals. Regular contributions require a different (annuity) formula.
