How interest works
Interest is the price of using someone else's money. When you save, the bank pays you interest for using your deposit. When you borrow, you pay the lender interest as a cost of the loan. The amount of interest depends on three factors:
- Principal (P) — the starting amount of money
- Rate (r) — the annual interest rate as a percentage
- Time (t) — how long the money is invested or borrowed
A fourth factor — compounding frequency — determines whether interest earns interest on itself, and how often. This is the key difference between simple and compound interest.
Simple vs. compound interest
Simple interest
I = P × r × t
Calculated only on the original principal. Interest stays constant each period. Used in some auto loans, personal loans, and Treasury bills. This simple interest calculator applies this formula.
Compound interest
A = P × (1 + r/n)nt
Calculated on principal plus accumulated interest. Your money grows exponentially over time. Used in savings accounts, CDs, credit cards, and most investments. This compound interest calculator supports any frequency.
Example: $10,000 at 5% for 10 years — simple interest earns $5,000 (total $15,000). Compound interest (monthly) earns $6,470 (total $16,470). That's $1,470 more from compounding alone.
Interest-only payments explained
An interest-only payment covers just the interest charges without reducing the principal balance. Use this interest only calculator to find your payment:
Monthly Interest-Only = (Principal × Annual Rate) ÷ 12
Example: A $400,000 mortgage at 6.5% → ($400,000 × 0.065) ÷ 12 = $2,167/month interest-only. Compare this to a fully amortizing 30-year payment of $2,528/month — the interest-only option saves $361/month but doesn't build equity.
When interest-only makes sense: HELOCs, investment property financing where cash flow matters more than equity, bridge loans, or temporary periods before refinancing. Most interest-only loans convert to fully amortizing after 5–10 years.
The power of compound interest
$10,000 invested at 5% (compounded monthly) grows dramatically over time. The longer you stay invested, the more compounding accelerates your returns:
| Years | Simple | Compound | Difference |
|---|---|---|---|
| 5 | $12,500 | $12,834 | +$334 |
| 10 | $15,000 | $16,470 | +$1,470 |
| 20 | $20,000 | $27,126 | +$7,126 |
| 30 | $25,000 | $44,677 | +$19,677 |
After 30 years, compound interest earns more than 3× the simple interest amount. This is why starting to invest early matters so much — even small amounts grow significantly over decades.
Rule of 72
The Rule of 72 is a quick way to estimate how long it takes your money to double:
Years to Double ≈ 72 ÷ Interest Rate
| Rate | Years to Double | $10K Becomes |
|---|---|---|
| 4% | 18 years | $20,000 |
| 6% | 12 years | $20,000 |
| 8% | 9 years | $20,000 |
| 10% | 7.2 years | $20,000 |
Interest on common amounts
How much interest on 1 million dollars? Annual interest earned at common rates (compounded annually, 1 year):
| Principal | At 4% | At 5% | At 6% |
|---|---|---|---|
| $100K | $4,000 | $5,000 | $6,000 |
| $500K | $20,000 | $25,000 | $30,000 |
| $1M | $40,000 | $50,000 | $60,000 |
At 5%, interest on $1 million is $50,000 per year — or about $4,167 per month. Monthly interest-only on $100K at 5%: $417. These figures assume no additional contributions and annual compounding.
FAQs
What is interest?
Interest is the cost of borrowing money — or the return earned on savings and investments. When you deposit money in a savings account, the bank pays you interest for using your funds. When you take out a loan, you pay the lender interest. Interest is expressed as a percentage rate (e.g., 5% per year) and can be calculated as simple or compound.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal: I = P × r × t. Compound interest is calculated on the principal plus previously earned interest, so your money grows exponentially. For example, $10,000 at 5% for 10 years: simple interest earns $5,000 (total $15,000), while compound interest (monthly) earns $6,470 (total $16,470). The longer the time period, the bigger the difference.
What is an interest-only payment?
An interest-only payment covers only the interest charges on a loan without reducing the principal balance. For a $300,000 mortgage at 6%, the monthly interest-only payment is $1,500 ($300,000 × 0.06 ÷ 12). Interest-only loans have lower monthly payments initially but you don't build equity. They're common in HELOCs, some ARMs, and investment property loans.
How much interest does $1 million earn?
At current savings rates: a high-yield savings account at 4.5% APY would earn approximately $45,000 per year ($3,750/month) on $1 million. At 5%: $50,000/year. In a CD at 5.25%: about $52,500/year. In stocks (historical 10% average): $100,000/year, though with much more risk and volatility. The interest on 1 million dollars varies significantly by investment type and current rates.
What is the Rule of 72?
The Rule of 72 is a quick mental math shortcut to estimate how long it takes for an investment to double. Divide 72 by the annual interest rate: 72 ÷ rate = years to double. At 6%: 72 ÷ 6 = 12 years. At 8%: 72 ÷ 8 = 9 years. At 12%: 72 ÷ 12 = 6 years. This works well for rates between 2% and 15%. It's an approximation — the exact time uses logarithms.
How does compounding frequency matter?
More frequent compounding produces slightly more interest because interest starts earning interest sooner. $10,000 at 5% for 10 years: annually = $16,289, quarterly = $16,436, monthly = $16,470, daily = $16,487. The difference between annual and monthly is meaningful, but monthly vs. daily is minimal. Most savings accounts compound daily; most loans compound monthly.
Is interest income taxable?
Yes — interest earned from bank accounts, CDs, bonds, and lending is generally taxable as ordinary income. Banks report interest over $10 on Form 1099-INT. Municipal bond interest is exempt from federal tax (and often state tax if issued in your state). Interest in tax-advantaged accounts (401k, IRA, Roth IRA) is tax-deferred or tax-free. Interest paid on student loans and mortgages may be tax-deductible.
What is the difference between APR and interest rate?
The interest rate is the base cost of borrowing. APR (Annual Percentage Rate) includes the interest rate plus fees, points, and other costs, expressed as a yearly rate. APR is always equal to or higher than the interest rate. For savings, APY (Annual Percentage Yield) accounts for compounding — it's always equal to or higher than the stated rate. Compare APRs for loans and APYs for savings to make fair comparisons.
How do you calculate monthly interest?
Divide the annual interest rate by 12 and multiply by the balance. Monthly interest = (Principal × Annual Rate) ÷ 12. For a $50,000 balance at 5%: ($50,000 × 0.05) ÷ 12 = $208.33 per month. For compound interest on savings, the bank applies this monthly and adds it to your balance, so next month's interest is calculated on a slightly higher amount.
What is accrued interest?
Accrued interest is interest that has been earned or incurred but not yet paid or received. For bonds, if you buy a bond between interest payment dates, you pay the seller the accrued interest since the last payment. For loans, accrued interest accumulates daily between payments. In accounting, accrued interest appears as a receivable (asset) or payable (liability) on the balance sheet.