How Does Compound Interest Work? (With Formula and Examples)

What Is Compound Interest?

Compound interest is interest calculated on both the original principal and the interest already earned. Each period, the interest earned gets added to the balance, and the next period's interest is calculated on that larger number.

Simple interest never does this. It always calculates against the original principal only.

Example with $5,000 at 6% annual interest over 3 years:

The gap looks small at three years. Extend it to 30, and simple interest gives you $14,000 while compound interest gives you $28,717 at the same rate. The difference is entirely due to earning interest on interest.

Compound interest is the process of earning interest on a growing balance that already includes previously earned interest -- the longer money compounds, the wider the gap becomes compared to simple interest.

The Compound Interest Formula

The standard formula is:

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

• A = final amount (principal + interest)
• P = principal (starting balance)
• r = annual interest rate as a decimal (6% = 0.06)
• n = number of compounding periods per year
• t = time in years

Example: $10,000 invested at 5% compounded monthly for 10 years:

• P = 10,000 | r = 0.05 | n = 12 | t = 10
• A = 10,000 × (1 + 0.05/12)^(12×10) = 10,000 × (1.004167)^120 = $16,470

The same $10,000 at 5% simple interest over 10 years: $15,000. Compounding adds $1,470 at no extra cost.

Run your own numbers with the OnSumo Compound Interest Calculator -- it handles all four compounding frequencies and outputs a year-by-year growth table.

The compound interest formula A = P(1 + r/n)^(nt) calculates the total value of an investment or debt by raising the periodic growth factor to the total number of compounding periods.

How Compounding Frequency Affects Growth

The variable n in the formula controls how often interest is added to the balance. More frequent compounding means slightly higher returns.

$10,000 at 6% over 10 years by compounding frequency:

Daily compounding beats annual by $312 on this balance -- meaningful at scale, but the interest rate matters far more than the frequency. A 7% annual rate compounded annually ($19,672) beats 6% compounded daily ($18,220) by over $1,400.

Use the OnSumo Compound Interest Calculator to compare frequencies side by side with your actual numbers.

Compounding frequency determines how many times per year interest is added to the principal -- daily compounding produces slightly more than monthly, but the interest rate has a much larger effect on the final balance than the frequency does.

The Rule of 72: A Fast Mental Check

Divide 72 by the annual interest rate to estimate how many years it takes to double your money.

• At 6%: 72 / 6 = 12 years to double
• At 9%: 72 / 9 = 8 years to double
• At 12%: 72 / 12 = 6 years to double

This works in reverse for debt. A credit card at 24% APR doubles the balance in 3 years if you make no payments (72 / 24 = 3).

The Rule of 72 is an approximation, accurate within one year for rates between 6% and 10%. For exact figures, use the OnSumo Compound Interest Calculator.

The Rule of 72 estimates the doubling time for a compounding balance by dividing 72 by the annual interest rate -- a quick mental check that works for both savings growth and debt accumulation.

Compound Interest on Debt

The same math that grows investments also grows debt. A $5,000 credit card balance at 22% APR with a 2% minimum payment takes more than 30 years to pay off and costs over $10,000 in interest -- more than double the original balance.

Mortgages also use compounding, though the structure is different: your monthly payment covers accrued interest first, then reduces principal. The OnSumo Mortgage Amortization Calculator shows exactly how each payment splits between interest and principal, and how extra payments collapse the total interest cost.

On the debt side, compounding favors the lender. On the savings side, it favors you. The variable is which side of the equation you are on.

Compound interest on debt works against borrowers -- interest accrues on the outstanding balance each period, which grows unless payments exceed the interest charges, so high-rate balances can grow faster than minimum payments can reduce them.

Frequently Asked Questions