💹 Interest Calculator
Work out the interest a deposit earns under simple or compound rules, at any compounding frequency, and see exactly how far apart the two methods end up.
Simple interest, compound interest, and why the gap keeps widening
Simple interest is paid on the original deposit and nothing else. Put $10,000 in an account paying 5% simple interest and it earns $500 a year, every year, whether the balance has grown to $12,000 or not. Compound interest is paid on the balance, which includes the interest already credited, so the amount earning interest keeps getting bigger.
Over one year the difference is almost invisible. Over thirty it is the whole story. The calculator above runs both so you can see the gap for your own numbers rather than take anyone's word for it.
The formulas
Simple interest is a multiplication. Compound interest depends on how often interest is credited, with n compounding periods per year:
simple: A = P × (1 + r × t) compound: A = P × (1 + r/n)n×t
P is the starting amount, r the annual rate as a decimal, t the number of years. Continuous compounding is the limit as n grows without bound, giving A = P × er×t. It is the theoretical ceiling, and daily compounding is already within a rounding error of it.
$10,000 at 5% for 10 years
| Method | Interest earned | Final balance |
|---|---|---|
| Simple interest | $5,000 | $15,000 |
| Compounded annually | $6,289 | $16,289 |
| Compounded quarterly | $6,436 | $16,436 |
| Compounded monthly | $6,470 | $16,470 |
| Compounded daily | $6,487 | $16,487 |
| Compounded continuously | $6,487 | $16,487 |
Two things are worth noticing. Compounding beats simple interest by $1,289 over the decade, nearly 26% more interest for no extra deposit. And the jump from annual to monthly compounding is worth $181, while the jump from monthly to daily is worth $17. Compounding frequency matters far less than people expect; the rate and the term do the heavy lifting.
How the gap grows with time
| Years | Simple | Compound | Difference |
|---|---|---|---|
| 1 | $10,600 | $10,617 | $17 |
| 5 | $13,000 | $13,489 | $489 |
| 10 | $16,000 | $18,194 | $2,194 |
| 20 | $22,000 | $33,102 | $11,102 |
| 30 | $28,000 | $60,226 | $32,226 |
Simple interest grows in a straight line; compound interest grows exponentially. After thirty years the compound balance is more than twice the simple one, and the gap is larger than the original deposit.
Where each one is actually used
- Simple interest: most car loans and personal loans in the US, short-term promissory notes, some bonds' coupon calculations, and statutory interest on late payments.
- Compound interest: savings accounts, certificates of deposit, mortgages, credit cards and essentially every investment product.
Credit cards compound daily on the balance, which is why a 22.9% APR costs closer to 25.7% over a year. The same mechanism that builds a savings balance quietly inflates a card debt.
The rule of 72
Divide 72 by the interest rate as a whole number to get the rough number of years for money to double. At 5%, about 14.4 years against an exact 14.2. At 9%, eight years. The approximation holds well between about 4% and 12% and drifts outside that range, and it works just as well for inflation running against you as for interest running for you.
A worked example
$25,000 placed for 7 years at 4.75% compounded monthly reaches $34,869, so $9,869 of interest, at an effective annual yield of 4.855%. The same money under simple interest would earn $8,313, so compounding is worth $1,556. Shifting the compounding to daily would add a further $14, while raising the rate by a quarter point would add $630.
Frequently Asked Questions (FAQs)
What is the difference between the interest rate and the APY?
The nominal rate is the headline number before compounding is taken into account. The annual percentage yield is what you actually earn over a year once compounding is applied. A 5% nominal rate compounded monthly produces an APY of 5.12%. Savings accounts are normally advertised by APY, which is why two accounts quoting the same nominal rate can pay different amounts.
How long does it take for money to double?
Divide 72 by the interest rate as a whole number. At 5%, money doubles in roughly 14.4 years; the exact figure is 14.2. The rule of 72 is accurate to within a few months for rates between about 4% and 12%.
Does this calculator account for tax or inflation?
No. It returns gross nominal interest. Interest income is usually taxable in the year it is credited, and inflation erodes what the final balance buys. For a real, after-inflation figure, run the result through the inflation calculator.
Should I use this for a loan instead of a deposit?
The compound formula is the same, but loans are repaid in instalments rather than left to grow, so the balance falls instead of rising. For borrowing, use the loan calculator or the amortization calculator, which handle repayments properly.
Why does continuous compounding barely beat daily?
Because the series converges fast. Going from annual to monthly captures most of the available benefit, monthly to daily captures a sliver, and daily to continuous captures almost nothing. At 5% over 10 years the difference between daily and continuous on $10,000 is about $1.
Is simple interest ever better for the borrower?
Yes. On a loan, simple interest means you never pay interest on interest, so a simple-interest loan costs less than a compounding one at the same rate. Most US car and personal loans use simple interest, which is also why paying early on them always saves money.
What happens if I add money regularly?
This calculator handles a single lump sum. For a starting balance plus regular contributions, use the compound interest calculator, which runs both the growth of the initial deposit and the growth of the contribution stream.