Interest basics Updated November 2026

APR vs APY

APR (annual percentage rate) is the simple yearly rate: the periodic rate times the number of periods. APY (annual percentage yield) is what you actually earn or pay in a year once compounding is included: APY = (1 + APR/n)^n - 1. APY is always at least as high as APR.

Syntax

APY = (1 + APR/n)^n - 1   APR = n x ((1 + APY)^(1/n) - 1)

Part	What it is
`APR`	Nominal annual rate as a decimal
`n`	Compounding periods per year
`APY`	Effective annual rate as a decimal

Examples

APR 12%, compounded monthly
APY = (1 + 0.12/12)^12 - 1

Result: APY = 12.68%

Excel: =EFFECT(12%, 12)

APR 5%, compounded quarterly
APY = (1 + 0.05/4)^4 - 1

Result: APY = 5.09%

Excel: =EFFECT(5%, 4)

APR 6%, compounded daily
APY = (1 + 0.06/365)^365 - 1

Result: APY = 6.18%

Common mistakes

Comparing a savings account quoted in APY with a loan quoted in APR as if they were the same measure; convert both to APY (effective rate) first.
Assuming the APR on a credit card is what you pay: an 18% APR compounded monthly on a carried balance costs 19.56% a year.
Reading the mortgage APR as the note rate: in the US, mortgage APR also folds in fees and points, so it is higher than the interest rate on the loan.

Practice APR vs APY

These drills check your answer on live data, free, no account needed.

Effective rate from a monthly APRA store credit card charges 6.25% APR, compounded monthly. What is the effective annual rate?
Effective rate with daily compoundingA short-term business line of credit charges 8.25% APR, compounded daily on a 365-day year. What is the effective annual rate?
APR implied by a paymentA lender offers $10,500 to be repaid in 36 monthly payments of $361.62. What APR (the monthly rate × 12) does this payment imply?

Questions

Which is better for a savings account, higher APR or higher APY?

APY is the number to compare because it reflects what you actually earn in a year. Two accounts with the same APR but different compounding frequencies have different APYs.

Is APY the same as the effective annual rate (EAR)?

Yes for deposits. APY and EAR are both (1 + r/n)^n - 1. APY is the consumer banking label; EAR is the finance textbook label.

Effective annual rateThe effective annual rate turns a nominal rate with monthly, quarterly or daily compounding into the true yearly rate: (1 + i/m)^m - 1. Examples and Excel.
Compound interestThe compound interest formula A = P(1 + r/n)^(nt), what each symbol means, examples for yearly and monthly compounding, the Excel FV function and errors.
Continuous compoundingContinuous compounding uses A = P x e^(rt), the limit of compounding infinitely often. Examples, the effective rate e^r - 1, doubling time and Excel EXP.
Mortgage payment formulaHow to calculate a monthly mortgage payment with M = P x r / (1 - (1 + r)^-n). Examples for 200,000 at 6% and 300,000 at 5%, Excel PMT and common mistakes.