Interest Rates Explained
What does this interest rate really mean?
Banks and lenders show rates in different ways, which makes them hard to compare. Convert between APR and APY to compare fairly, and see how quickly a rate doubles your money.
How to use this calculatorShowHide
- Step 1: Pick a direction: turn an APR into an APY, or the other way round.
- Step 2: Enter the rate and how often interest is added (monthly is most common).
- Step 3: Below, enter any yearly return to see how many years it takes to double your money.
What you'll need
- A rate from a bank, card or loan offer — and whether it says APR or APY
Don't know a number? Leave the example value in, or tap the ⓘ next to it. New to this? Read the Beginner's Guide →
APY (effective annual yield)
5.1162%
An APR of 5.0000% compounded monthly is the same as an APY of 5.1162%. Compare savings accounts by APY and loans by APR — but remember a loan's true yearly cost is its APY.
- APR
- 5.0000%
- APY
- 5.1162%
- Compounding boost
- 0.1162%
- APY − APR
Doubling time
Rule of 72 estimate
9.00 years
Exact: ln 2 ÷ ln(1 + r)
9.006 years
At 8.00% a year, money doubles in 9.006 years. The Rule of 72 (72 ÷ 8) estimates 9 years — almost exactly right. The shortcut works best for rates around 6%–10%; it drifts at very low or very high rates because it approximates the natural logarithm ln(1 + r) with a straight line.
Same APR, different compounding
| Compounding | APY |
|---|---|
| Annually | 5.0000% |
| Semi-annually | 5.0625% |
| Quarterly | 5.0945% |
| Monthly | 5.1162% |
| Bi-weekly | 5.1221% |
| Weekly | 5.1246% |
| Daily | 5.1267% |
| Continuous | 5.1271% |
What this means
In plain English
Rates can be shown in two ways, which makes them confusing to compare:
- APR is the basic yearly rate. Loans and credit cards show APR.
- APY also counts the interest you earn (or pay) on interest during the year, so it's a little higher. Savings accounts show APY.
The Rule of 72 is a handy shortcut: divide 72 by a yearly rate to see roughly how many years it takes to double your money.
When to use it
- Comparing a savings account (APY) with a loan (APR) fairly
- Understanding why a credit card's 24% APR costs you more than 24% a year
- Quickly estimating how long it takes money to double
Example
A 5% APR with interest added monthly works out to a 5.12% APY (5.1162% exactly).
At 8% a year, the Rule of 72 says your money doubles in 72 ÷ 8 = 9 years. The exact answer is 9.006 years — almost the same. The shortcut is less accurate at very low or very high rates: at 1% it says 72 years (really about 70), and at 30% it says 2.4 years (really about 2.6).
Watch out for
Comparing an APR to an APY. Banks show savings accounts by APY (the bigger number) and loans by APR (the smaller number). Convert them to the same type before comparing.
The math (optional)
- APY = (1 + APR ÷ n)^n − 1, where n is how many times a year interest is added
- APR = n × ((1 + APY)^(1/n) − 1)
- Continuous compounding: APY = e^APR − 1
- Exact doubling time: ln 2 ÷ ln(1 + rate); Rule of 72: 72 ÷ rate in percent