How Loan Interest Works

Interest is the price of borrowing money, and the rent you earn when you lend it. Every loan, credit card, mortgage and savings account uses the same few building blocks, but small differences in how interest is calculated can change what you pay by thousands. This guide explains those building blocks in order, with worked examples you can reproduce in our calculators.

Simple interest: the starting point

Simple interest is charged only on the original amount, the principal:

interest = principal × rate × time

Borrow $10,000 at 6% a year for 3 years with simple interest and you pay 10,000 × 0.06 × 3 = $1,800 in interest. Simple interest is common for short-term loans, some car loans and bonds. The simple interest calculator also handles rates quoted per month and terms in days.

Compound interest: interest on interest

With compound interest, each period’s interest is added to the balance, and the next period’s interest is charged on the larger amount:

balance = principal × (1 + rate ÷ n)^(n × years)

where n is the number of compounding periods a year. The same $10,000 at 6% for 3 years:

• Compounded yearly: 10,000 × 1.06³ = $11,910.16, so $1,910.16 of interest.
• Compounded monthly: 10,000 × 1.005³⁶ = $11,966.81, so $1,966.81 of interest.

Compounding works for you in savings and against you in debt. Unpaid credit card interest compounds, which is why a balance can grow even when you aren’t spending. You can see the effect over long periods in the compound interest calculator.

APR vs. APY

• APR (annual percentage rate) is the yearly rate before compounding, plus certain fees on loans.
• APY (annual percentage yield), or effective annual rate, includes compounding.

A 6% APR compounded monthly is (1 + 0.06 ÷ 12)¹² − 1 = 6.17% APY. When you compare offers, compare APR with APR and APY with APY.

How an amortized loan payment works

Most personal loans, car loans and mortgages are amortizing. You pay the same amount every month, and each payment covers that month’s interest first, with the rest reducing the balance. The fixed payment comes from this formula:

payment = P × r ÷ (1 − (1 + r)^−n)

P is the principal, r is the monthly rate (annual rate ÷ 12), and n is the number of payments. In South Asia this payment is usually called the EMI (equated monthly installment). It is the same formula, and the EMI calculator uses it.

Worked example: a $300,000 mortgage

A $300,000 mortgage at 6.5% over 30 years (360 payments):

1. Monthly rate: 0.065 ÷ 12 = 0.0054167.
2. Payment: 300,000 × 0.0054167 ÷ (1 − 1.0054167⁻³⁶⁰) = $1,896.20 a month.
3. Month 1: interest is 300,000 × 0.0054167 = $1,625.00, so only $271.20 reduces the balance.
4. Over 30 years you pay $382,633 in interest, more than the loan itself.

The same loan over 15 years costs $2,613.32 a month, but the total interest falls to $170,398, saving over $212,000. The mortgage calculator adds property tax and insurance so you see the full monthly cost, and the loan calculator works for any fixed-rate loan.

Flat rate vs. reducing balance

Some lenders, especially for car finance and consumer loans, quote a flat rate. It is charged on the original amount for the whole term, even though you are paying the loan down:

• Flat 10% on 100,000 for 3 years: interest = 100,000 × 0.10 × 3 = 30,000, so the monthly payment is 130,000 ÷ 36 = 3,611.11.
• The reducing-balance rate that gives the same payment is about 17.9%.

A flat rate looks almost half as expensive as it really is. Always ask for the reducing-balance rate or the APR before you sign.

Credit cards: the most expensive compounding

Credit cards charge interest on the balance you carry from month to month, usually at a high APR, and the minimum payment is set low on purpose. A common formula is 1% of the balance plus that month’s interest, with a floor of about $25.

Worked example: a $5,000 balance at 22% APR

• The monthly rate is 22% ÷ 12 = 1.833%, so the first month’s interest is $91.67.
• Paying only the minimum (1% of the balance plus interest, at least $25) takes about 19 years to clear the card, and you pay about $8,100 in interest, more than the original $5,000.
• Paying a fixed $200 a month instead clears it in 34 months and costs about $1,750 in interest.

The difference comes entirely from how fast the balance falls. A minimum payment that shrinks as the balance shrinks keeps the debt alive for decades. If you carry a balance, set a fixed payment that you never reduce.

How to pay less interest

1. Choose a shorter term if the payment fits your budget. The rate is often lower too.
2. Make extra payments early. Adding $200 a month to the 30-year mortgage above clears it in about 23 years instead of 30 and saves about $103,000 in interest.
3. Improve your credit score before applying. A 1-point lower rate on a large loan is worth more than almost any other saving.
4. Compare the APR, not just the rate. It includes many of the fees.
5. Avoid compounding debt. Pay credit cards in full, or move balances to a lower fixed rate.

A quick way to estimate growth: the rule of 72

Divide 72 by the annual rate to estimate how many years it takes for money or debt to double. At 6%, 72 ÷ 6 = 12 years. The exact answer is 11.9. At 18%, typical of credit cards, an unpaid balance doubles in about 4 years.

Common mistakes

• Comparing monthly payments instead of total cost. A longer term always looks cheaper per month.
• Ignoring fees. An origination fee taken out of the loan raises the true cost. The APR captures it.
• Assuming extra payments go to principal. Some lenders apply them to future payments instead. Ask them to apply extra payments to principal.
• Confusing a flat rate with a reducing-balance rate. Convert before you compare.

Once you know whether interest is simple, compound or amortized, and on what balance it is charged, any loan offer becomes easy to compare. Put the numbers into the calculators linked here, and look at the total interest line before you decide.

Frequently asked questions

Why is most of my early loan payment interest?

Interest is charged on the balance you still owe, which is largest at the start. On a $300,000 mortgage at 6.5%, the first month's interest is $1,625 of a $1,896.20 payment. As the balance falls, more of each payment goes to principal.

What is the difference between APR and APY?

APR is the yearly rate before compounding. APY (or effective annual rate) includes compounding. A 6% APR compounded monthly is a 6.17% APY. Lenders tend to advertise APR on loans, and banks advertise APY on savings, because each makes their number look better.

Is a flat interest rate the same as a normal interest rate?

No. A flat rate charges interest on the original amount for the whole term, even as you repay it. A 10% flat rate over 3 years costs about the same as a 17.9% reducing-balance rate.

Do extra payments really make a difference?

Yes, especially early on. Adding $200 a month to a $300,000, 30-year mortgage at 6.5% pays it off about 7 years sooner and saves over $103,000 in interest, as long as the lender applies the extra to principal.

What is the rule of 72?

A quick way to estimate doubling time. Divide 72 by the yearly interest rate. At 6%, money (or debt) doubles in about 72 ÷ 6 = 12 years. The exact answer is 11.9 years.