How the interest calculator works
Interest is the price of money. When you save, the bank pays you interest. When you borrow, you pay it. This calculator works out the interest you earn on savings in two ways, so you can see the difference.
- Simple interest is paid only on the money you put in. The interest never earns interest of its own.
- Compound interest is added to your balance, so next period you earn interest on the interest too. Over long periods this makes a big difference.
You can add a regular deposit each month or year, choose how often interest compounds, take tax off the interest, and see the result in today’s money after inflation.
The formulas
Compound interest: A = P × (1 + r ÷ n)^(n × t)
P = principal, r = yearly rate as a decimal, t = years, n = compounding periods a year
With simple interest, each deposit earns r × the time left after it is paid in. With compound interest, the calculator steps through each month at the equivalent monthly rate. At year ends this gives exactly the same answer as the textbook formula.
Tax is taken from each interest payment as it is earned, so it also slows the compounding. Buying power divides the ending balance by (1 + inflation)^years to show what it would buy at today’s prices.
Worked example 1: simple interest
You lend or deposit $5,000 at 6% simple interest for 18 months.
- Interest = $5,000 × 0.06 × 1.5 = $450
- Total at the end = $5,450
Simple interest grows in a straight line: the same $25 each month, however long you wait.
Worked example 2: compound vs simple with deposits
Start with $20,000, add $200 at the end of each month, and earn 5% a year for 10 years. This is the calculator’s default.
| Compound (monthly) | Simple | |
|---|---|---|
| Paid in | $44,000 | $44,000 |
| Interest on the $20,000 | $12,940 | $10,000 |
| Interest on the deposits | $7,056 | $5,950 |
| Ending balance | $63,997 | $59,950 |
Compounding earns about $4,047 more over 10 years. The gap keeps widening each year, because the extra interest earns interest too.
If 25% of the interest goes to tax, the compound balance ends at about $58,148. At 3% inflation, the untaxed $63,997 has the buying power of about $47,620 today.
Worked example 3: a classic textbook check
$1,000 at 5% for 3 years:
- Simple: $1,000 × 0.05 × 3 = $150 of interest, $1,150 in total.
- Compounded yearly: $1,000 × 1.05³ = $1,157.63.
The difference is small over three years. Over decades it is huge.
How the gap grows over time
The table shows $10,000 at 5% with no deposits, simple interest against interest compounded once a year.
| Years | Simple interest balance | Compound interest balance | Extra from compounding |
|---|---|---|---|
| 1 | $10,500 | $10,500 | $0 |
| 5 | $12,500 | $12,763 | $263 |
| 10 | $15,000 | $16,289 | $1,289 |
| 20 | $20,000 | $26,533 | $6,533 |
| 30 | $25,000 | $43,219 | $18,219 |
After 30 years, compounding has earned more than twice as much interest as simple interest. The SEC’s Investor.gov explains the same effect in its guide to compound interest. It works against borrowers in the same way.
Compounding frequency and APY
More frequent compounding adds a little more. 5% compounded monthly is an effective annual rate of 5.116%, while 5% compounded daily is 5.127%. Banks in the US must show this effective rate as the APY (annual percentage yield) under the Truth in Savings Act. The calculator shows the APY for compound interest so you can compare accounts. If your bank quotes an APY, enter it with yearly compounding to get the same result.
Where each type of interest is used
- Savings accounts, CDs and money market accounts compound, usually daily or monthly.
- Investments that reinvest their earnings, such as funds that reinvest dividends, behave like compound interest.
- Many car loans and some personal loans charge simple interest on the balance you still owe.
- Bonds pay fixed coupons on their face value. The coupons only compound if you reinvest them.
- Credit cards compound: interest is charged daily on a balance that includes past interest. That is why card debt grows so fast.
Tips
- Compare by APY, not the headline rate. It is the true yearly yield.
- Start early. Time is the strongest part of the compound formula.
- Count the tax. Interest in a regular savings account is taxed each year. Tax-advantaged accounts can let it compound in full.
- Check against inflation. If your after-tax rate is below inflation, your money is losing buying power even as the balance grows.
- Remember it cuts both ways. The same maths makes debt expensive. Pay off high-rate debt before chasing a slightly better savings rate.
Related calculators
For long-term savings with doubling time and the rule of 72, use the compound interest calculator. To lock in a fixed rate, try the CD calculator. To plan a savings goal, use the savings calculator. To see what interest costs when you borrow, use the loan calculator.
This calculator assumes a steady rate for the whole period. It is for education and planning, not financial or tax advice.