Simple vs Compound Interest: Differences, Formulas and Examples

Two accounts can advertise the same interest rate and still grow very differently, because one pays simple interest and the other pays compound interest. Knowing which is which decides how much you earn on savings, and how much you owe on some loans. This guide compares them side by side, with the formulas and numbers you can verify.

Simple interest

Simple interest is calculated only on the original amount, called the principal. The formula is I = P × r × t, where P is the principal, r is the yearly rate as a decimal and t is the time in years. The total amount is P + I.

Invest $5,000 at 4 percent simple interest for three years and you earn 5,000 × 0.04 × 3 = $600, ending with $5,600. Every year adds the same $200. If you plot the balance over time you get a straight line.

Compound interest

Compound interest is calculated on the principal plus all the interest already added. The formula is A = P × (1 + r ÷ n)^(n × t), with n as the number of times a year interest is added. The balance follows a curve that gets steeper over time.

The same $5,000 at 4 percent compounded monthly for three years grows to $5,636.36, which is $36.36 more than with simple interest. That looks small, and over three years it is. The gap widens with time.

Side by side: $10,000 at 5 percent

• After 3 years: simple $11,500; compound (yearly) $11,576.25
• After 10 years: simple $15,000; compound (yearly) $16,288.95
• After 30 years: simple $25,000; compound (yearly) $43,219.42

After 30 years the compounding account holds almost twice as much. The difference is entirely interest earning interest.

Which one applies to my product?

Most everyday products compound:

• Savings accounts, certificates of deposit and money market accounts add interest to the balance, usually monthly or daily.
• Credit cards and most mortgages charge interest that is added to the balance you owe.
• Investment returns compound as gains stay invested.

Simple interest appears in specific places:

• Some car and personal instalment loans calculate interest daily on the outstanding principal without adding it to the balance.
• Treasury bills, some bonds and fixed coupon payments pay a set interest amount.
• Short-term loans between individuals, and late-payment charges expressed as a percentage.
• Textbook and exam questions.

Converting time units

Simple interest formulas need time in years. Six months is 0.5, three months is 0.25, and 90 days is 90 ÷ 365 = 0.2466. So $10,000 at 6 percent for 90 days earns 10,000 × 0.06 × 0.2466 = $147.95. Some contracts use a 360-day year, which raises the interest slightly, so check the day-count convention in the agreement.

APR and APY

Two labels help compare products. APR (annual percentage rate) is the yearly rate without compounding effects, used for loans. APY (annual percentage yield) includes compounding and is used for savings. A savings account with a 5.00 percent rate compounded monthly has an APY of about 5.12 percent. When you compare savings products, use APY; when you compare loans, use APR.

Why it matters when you borrow

For borrowers, compounding is a cost. A loan or card that adds interest to the balance charges you interest on interest. A loan with simple interest on the reducing balance charges only on what you owe today. That is why a payment that covers less than the interest each month makes a compounding debt grow.

Use the calculators

The Simple Interest Calculator accepts years, months or days, shows the formula with your numbers and lists simple and compound growth side by side. For interest that compounds with regular deposits, use the Compound Interest Calculator. The Loan Calculator and EMI Calculator handle repayments, and the Percentage Calculator is useful for checking the arithmetic. For the full story of compounding, read how compound interest works.