What the three numbers mean
Simple against compound, year by year
| After | Simple | Compound | Difference |
|---|
Interest is rent on money. How much of it you pay depends on three things: the amount, the rate, and how the balance behaves over time. The last one is where most of the confusion lives, so this page shows the same money three ways.
Simple interest
Interest on the original amount only: principal × rate × time. $10,000 at 9.5% for three years is $2,850. Nothing is charged on interest already owed. This is how most car loans, personal loans and student loans describe themselves, and it is the fairest kind for a borrower.
Compound interest
Interest is added to the balance, and then earns interest itself. The more often that happens, the more it costs. Over short periods the difference is small; over long ones it is enormous, which is why compounding is wonderful in a savings account and expensive on a credit card.
Credit cards compound daily, using the average daily balance. Savings accounts compound too, which is why they advertise an APY rather than a rate.
Interest on a loan you are repaying
This is the one that matters to most people, and it is neither of the above. On an amortizing loan you pay interest on the balance, and the balance falls every month, so the total interest is much less than simple interest on the original amount. The same $10,000 at 9.5% repaid monthly over three years costs about $1,530 in interest, not far off half the simple-interest figure.
If you want the full payment-by-payment picture, the amortization schedule calculator prints it.
Daily interest
Many loans accrue daily: the balance multiplied by the rate, divided by 365 (some lenders use 360). It is why paying a few days early saves a little, why paying late costs a little more, and why a payment made on the due date is not quite the same as one made a week before. The box above gives the daily figure for your balance.
Quick answers
How do I calculate interest on a loan?
For simple interest, multiply the amount by the rate by the time in years. For a loan you are repaying monthly, the interest each month is the balance times the annual rate divided by 12, and the balance falls each month.
What is the difference between simple and compound interest?
Simple interest is charged only on the original amount. Compound interest is charged on the interest as well, so it grows faster the more often it compounds.
How much interest will I pay on $10,000?
At 9.5% over three years: $2,850 as simple interest, about $3,280 if it compounds monthly and nothing is repaid, or about $1,530 if you repay it in equal monthly payments.
How is daily interest worked out?
The balance multiplied by the annual rate, divided by 365. Some lenders use 360 days, which makes each day slightly more expensive.
Is APR the same as the interest rate?
No. APR includes fees as well as interest, which is why it is usually the higher figure.
Sources
- CFPB, simple interest and precomputed interest
- CFPB, how card interest is calculated daily
- 12 CFR § 1030.2, the definition of annual percentage yield
- Federal Reserve G.19, average consumer credit rates