Equivalent interest rate calculator
Convert a compound interest rate between month, quarter, half-year and year.
Equivalent annual rate
1% per month is equivalent to 12.6825% per year with compound interest.
How this is calculated →- Quarterly3.0301%
- Semiannual6.152%
- Nominal annual rate (× 12, APR)12%
For compound interest. With simple interest the conversion is proportional (1% a month = 12% a year).
How to convert rates
With compound interest, a rate for one period becomes another by raising to a power: i₂ = (1 + i₁)^(n₂/n₁) − 1, with n in months. From 1% a month to a year: 1.01¹² − 1 = 12.6825%.
Going back uses the root: 12% a year is 1.12^(1/12) − 1 = 0.9489% a month. Multiplying the monthly rate by 12 gives the nominal rate (APR), which is lower than the effective rate (APY).
Frequently asked questions
What is 1% a month per year?
12.68% a year compounded (the APY). The 12% you get by multiplying by 12 is the nominal rate, or APR.
What is the difference between APR and APY?
APR is the nominal annual rate; APY is the effective annual rate including compounding. 12% APR compounded monthly is 12.68% APY.
Can I use it to compare loans and savings?
Yes. Convert every rate to the same basis (monthly or annual) before comparing.
Related calculators
- Compound interest Investment with monthly contributions
- Loan payment Monthly payment and schedule
- Savings goal Monthly saving for a goal
- Simple interest Interest and total (I = P × r × t)
- Financial calculator N, I/Y, PV, PMT and FV
- Marketplace profit Profit per sale and target price
- Inflation Dollar value over time, 1913 to today
- Margin and markup Profit margin and selling price