Interest Rate Calculator
Find the interest rate from balance changes, convert APR to APY for any compounding frequency, and calculate the effective annual rate. Supports daily through annual compounding.
Enter starting amount, ending amount, and time period to find the implied interest rate.
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How It Works
Enter starting value (PV), ending value (FV), and time period (years). Rate = (FV/PV)^(1/t) − 1. Example: $5,000 grew to $7,401 in 8 years: rate = (7401/5000)^(1/8) − 1 = 5.0%/yr. Works for investments, savings, or any quantity growing at a constant rate.
Rate = (FV/PV)^(1/t) − 1$5,000 → $7,401 in 8yr: rate=(7401/5000)^0.125−1=5.0%/yrSelect compounding frequency and enter APR. APY = (1 + APR/n)^n − 1. The results show APY for each common compounding frequency so you can see the impact. Use APY to compare savings accounts regardless of their stated compounding frequency.
APY = (1 + APR/n)^n − 15% APR: monthly APY=5.116%, daily APY=5.127%Enter your current savings (PV), target amount (FV), and time horizon. The calculator finds the required annual return rate. Example: turning $30,000 into $100,000 in 10 years requires 12.79%/yr — stock market average but not guaranteed. Adjusting time or target helps set realistic expectations.
Required rate = (FV/PV)^(1/t) − 1$30k → $100k in 10yr → need 12.79%/yr returnCredit cards compound daily on the outstanding balance. A 24% APR becomes APY = (1+0.24/365)^365 − 1 = 27.11%. This explains why minimum payments trap borrowers — interest compounds daily on the balance. Enter your credit card APR to see the true effective rate.
CC APY = (1 + APR/365)^365 − 124% APR CC: APY=27.11% | 18% APR: APY=19.72%Account A: 4.9% APR compounded daily. Account B: 5.0% APR compounded annually. APY of A = (1+0.049/365)^365−1 = 5.02%. APY of B = 5.0%. Account A actually earns more despite lower APR. Always compare APY, never APR, for savings decisions.
Compare APY not APR for savings accounts4.9% daily (APY=5.02%) beats 5.0% annual (APY=5.0%)Quick Reference
Verify these in the calculator above.
Find rate
$5k → $7,401 in 8yr
5.0%/yr rate
APR to APY
5% APR, monthly compound
APY = 5.116%
APR to APY
5% APR, daily compound
APY = 5.127%
Credit card
24% APR credit card, daily
APY = 27.11%
Goal rate
$30k → $100k in 10yr
Need 12.79%/yr
Rule of 72
Rule of 72: double in 10yr
Need ~7.2%/yr
Comparison
4.9% daily vs 5.0% annual
Daily wins (5.02% APY)
Real rate
Real rate at 5% rate, 3% inflation
~2%/yr real
Tips & Shortcuts
For savings comparisons, always use APY — it accounts for compounding and gives the true annual return. Banks are required to display APY for savings products.
For loan comparisons, use APR — but remember APR does not include all fees for mortgages. Use APR for standardized comparison, then calculate total cost for the final decision.
Credit cards with 20%+ APR compound daily — the true APY is significantly higher. Paying the full balance monthly avoids this entirely.
The Rule of 72 also works for rates: to double in 10 years, you need 72/10 = 7.2%/yr. To find rate needed for any doubling time: rate = 72/years.
For inflation-adjusted returns: real rate ≈ nominal rate − inflation. A 5% savings rate with 3% inflation gives only 2% real purchasing power growth.
Common Mistakes
Comparing APR across savings accounts instead of APY
APR ignores compounding. A 5% APR compounded daily (APY=5.127%) beats a 5% APR compounded annually (APY=5%). Use APY for savings, which banks are required to display.
Assuming the nominal rate = effective rate
5% APR ≠ 5% effective. The effective rate is APY, which is always at least as high as APR. For daily compounding at 5% APR, the effective rate is 5.127%.
Forgetting compounding when comparing credit card offers
A 21.99% APR credit card compounding daily has an effective APY of 24.6%. Use the calculator to find the true cost before accepting a credit card offer.
Using the wrong formula for compound vs simple interest
Compound rate: (FV/PV)^(1/t) − 1. Simple rate: (FV−PV)/(PV×t). Using the wrong formula gives a different rate. Most investments and loans use compound interest.
Entering monthly rate instead of annual rate
Most calculators expect annual rate. If a lender quotes a monthly rate (common for some personal loans), multiply by 12 to get the approximate annual rate (exact: (1+monthly)^12 − 1 = annual APY).
Frequently Asked Questions
Use the calculator with your starting balance, ending balance, and time period. Rate = (End/Start)^(1/t) − 1 for compound, or (End−Start)/(Start×t) for simple interest. Example: $1,000 grew to $1,276 in 5 years: rate = (1276/1000)^(0.2) − 1 = 5.0%/yr.
APR (Annual Percentage Rate) is the nominal rate without compounding. APY (Annual Percentage Yield) is the effective annual rate with compounding. APY = (1 + APR/n)^n − 1. At 5% APR: monthly compounding gives APY = 5.116%, daily gives 5.127%. Banks advertise APY on savings and APR on loans.
APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. For 6% APR: monthly (n=12): APY = (1.005)^12 − 1 = 6.168%. Daily (n=365): APY = (1+0.06/365)^365 − 1 = 6.183%.
Effective interest rate = APY = the actual annual rate earned or paid, accounting for compounding. It is what you actually earn on savings or actually pay on loans. Use effective rate for all comparisons.
US law (Truth in Lending Act) requires credit cards to disclose APR. However, credit cards compound daily, so the true cost is APY. A 24% APR credit card has APY = (1+0.24/365)^365 − 1 = 27.11%. This is why credit card debt is so expensive.
More frequent compounding gives higher effective rate. At 5% APR: annual APY=5.000%, monthly=5.116%, daily=5.127%. The difference between monthly and daily is tiny (0.011%). The nominal rate matters much more than compounding frequency for everyday decisions.
Enter starting balance (PV), target balance (FV), and time (t). Rate = (FV/PV)^(1/t) − 1 for annual compounding. Example: need $50,000 in 10 years, have $20,000 now: rate = (50000/20000)^(0.1) − 1 = 9.6%/yr. This tells you the return needed.
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