Compound Interest vs Simple Interest: What Is the Difference?

The formulas

Simple interest calculates only on the original principal:

A = P x (1 + r x t)

Compound interest recalculates on a growing balance each period:

A = P x (1 + r/n)^(nt)

Where P = principal, r = annual rate as a decimal, t = years, n = compounding periods per year.

Side-by-side comparison: $10,000 at 7% over different time periods

The difference is modest in the first decade and then accelerates. At 30 years, compound interest produces 2.6 times more than simple interest on the same starting amount at the same rate. At 40 years, 4.3 times more. This is why the distinction matters for long-term savings and is mostly irrelevant for a 3-month loan.

How simple interest works

Simple interest calculates on the original principal only, every period. Previous interest earned does not affect future calculations.

Example: $2,000 lent at 5% simple interest for 3 years.

• Year 1: $2,000 x 0.05 = $100 interest
• Year 2: $2,000 x 0.05 = $100 interest
• Year 3: $2,000 x 0.05 = $100 interest
• Total interest: $300
• Final amount: $2,300

The base ($2,000) never changes. Interest payments are flat and predictable.

How compound interest works

Compound interest adds earned interest to the balance at each compounding period. All future interest is calculated on this larger number.

Example: $2,000 deposited at 5% compounded annually for 3 years.

• Year 1: $2,000 x 0.05 = $100; new balance $2,100
• Year 2: $2,100 x 0.05 = $105; new balance $2,205
• Year 3: $2,205 x 0.05 = $110.25; new balance $2,315.25

Total interest: $315.25 vs. $300.00 with simple interest. A $15.25 difference over 3 years at 5%.

At 30 years, the same deposit and rate would produce a $50,000 difference. Time is the variable that makes compound interest consequential.

Which type applies to your situation

Knowing which type governs a financial product tells you whether the balance grows linearly or exponentially.

Simple interest applies to:

• Short-term personal loans from some lenders
• Some auto loans (check your loan agreement)
• US Treasury bills
• Most promotional "0% financing" store offers
• Some bonds paying fixed coupons without reinvestment

Compound interest earns for you in:

• Savings accounts
• Certificates of deposit (CDs)
• Money market accounts
• Retirement accounts (401k, IRA, Roth IRA)
• Index funds and ETFs where dividends are reinvested

Compound interest is charged against you in:

• Most credit cards (compounded daily or monthly)
• Mortgages
• Most private student loans
• Home equity loans and lines of credit

When in doubt, check the account agreement. The Truth in Savings Act, enforced by the Consumer Financial Protection Bureau, requires US depository institutions to disclose the APY (Annual Percentage Yield) and compounding frequency for all savings products. Loan documents must disclose the APR and compounding method under the Truth in Lending Act.

The debt side: compound interest on an unpaid balance

The same mechanism that grows savings also grows debt. The Federal Reserve's G.19 Consumer Credit report shows the average credit card APR at approximately 21.5% as of early 2026.

A $3,000 credit card balance at 22% APR (compounded monthly), with no payments made:

• After 1 year: approximately $3,731
• After 2 years: approximately $4,641
• After 3 years: approximately $5,771

The balance grew by $2,771 in three years from interest alone. Credit card issuers compound monthly: interest is added to your balance each billing cycle, and next month's interest is calculated on that higher number.

This is the same mechanism as a savings account, running in the opposite direction.

Why long-term investors need to understand the difference

The clearest application is retirement savings. At 7% annual return over 30 years on a $20,000 starting balance:

• Simple interest: $20,000 + ($20,000 x 0.07 x 30) = $62,000
• Compound interest (monthly): approximately $162,000

That is a $100,000 difference on the same starting amount at the same rate. Index fund investing compounds because gains accumulate on top of previous gains, especially when dividends are reinvested. The 7% figure represents the approximate inflation-adjusted historical return of the US stock market, based on Aswath Damodaran's annual returns dataset (NYU Stern, updated through 2024).

The practical implication: savings vehicles that compound (savings accounts, retirement accounts, investment accounts) produce exponential growth over time. Loans that compound (credit cards, mortgages) cost more than a simple-interest calculation would suggest.

For the detailed mechanics and formula breakdown, see The Compound Interest Formula. To model your specific scenario, use the Compound Interest Calculator: enter your starting balance and a monthly contribution amount to compare trajectories, or adjust the compounding frequency to see how it affects the final balance.