Simple interest
Simple interest is calculated only on the original principal, using I = P × r × t, where P is the principal, r is the annual rate as a decimal, and t is time in years. Because the base never changes, the interest earned each year is identical and total growth is linear.
Simple interest appears in short-term instruments, some car loans, most bonds' coupon payments, and many personal loans between individuals. It is also the correct model for any arrangement where interest is paid out rather than left to accumulate.
Compound interest
Compound interest adds each period's earnings to the balance, so subsequent interest is calculated on a larger amount. The annual-compounding formula is A = P(1 + r)^t; with n compounding periods a year it becomes A = P(1 + r/n)^(nt). Savings accounts, certificates of deposit, credit cards, and reinvested investment returns all compound.
The gap between the two widens with time. On $5,000 at 5% for 3 years, simple interest gives $750 while annual compounding gives about $788 — a difference of $38. Over 30 years the same principal yields $7,500 simple versus about $16,600 compound.
| After | Simple | Compound, annually | Compound, monthly | Monthly compounding gains |
|---|---|---|---|---|
| 1 year | $250 | $250 | $256 | $6 |
| 3 years | $750 | $788 | $807 | $57 |
| 5 years | $1,250 | $1,381 | $1,417 | $167 |
| 10 years | $2,500 | $3,144 | $3,235 | $735 |
| 20 years | $5,000 | $8,266 | $8,563 | $3,563 |
| 30 years | $7,500 | $16,610 | $17,339 | $9,839 |
APY: the rate after compounding
A nominal rate says nothing about how often it is applied. The annual percentage yield, or APY, is the rate you actually earn in a year once compounding is included, so it is the only fair way to compare accounts that compound differently. The calculator reports it whenever you choose compound interest.
| Compounded | APY | Interest in year one |
|---|---|---|
| Annually | 5.0000% | $500.00 |
| Semi-annually | 5.0625% | $506.25 |
| Quarterly | 5.0945% | $509.45 |
| Monthly | 5.1162% | $511.62 |
| Daily | 5.1267% | $512.67 |
| Continuously | 5.1271% | $512.71 |
Which model applies to you
Read the terms rather than assuming. Credit cards compound, usually daily, which is a large part of why card debt grows so quickly. Savings accounts and CDs compound, typically daily or monthly. Bonds generally pay simple interest as periodic coupons unless you reinvest them. Mortgages and most amortizing loans charge interest on the outstanding balance each period, which behaves like compounding from the lender's perspective even though the payment is fixed.
When comparing deposit accounts, use the annual percentage yield (APY) rather than the nominal rate. APY already accounts for compounding frequency, so it is directly comparable across accounts.
| Product | Model | Typical compounding |
|---|---|---|
| Savings account | Compound | Daily, credited monthly |
| Certificate of deposit | Compound | Daily or monthly |
| Credit card | Compound | Daily, on the outstanding balance |
| Mortgage or auto loan | Interest on the falling balance | Monthly, inside a fixed payment |
| Bond coupons | Simple, unless reinvested | Paid out semi-annually |
| Treasury bills, short notes | Simple (discount) | None — paid at maturity |
| Loan between individuals | Usually simple | As agreed |
Interest for part of a year
Both formulas take time in years, so shorter periods are entered as fractions. The calculator accepts months or days directly and converts them; the table shows the conversions it uses.
| Period | Calculation | Years |
|---|---|---|
| 30 days | 30 ÷ 365 | 0.0822 |
| 90 days | 90 ÷ 365 | 0.2466 |
| 6 months | 6 ÷ 12 | 0.5000 |
| 18 months | 18 ÷ 12 | 1.5000 |
| 2 years 3 months | 27 ÷ 12 | 2.2500 |