Simple vs. Compound Interest Explained

February 17, 2026 |

finance interest

Simple interest is calculated on the original principal only. Compound interest is calculated on the principal plus all previously earned interest. That one difference produces very different results over time.

The simple interest formula

I = P x r x t

Where:

I = interest earned
P = principal (starting amount)
r = annual interest rate (as a decimal)
t = time in years

The total amount after t years is: A = P + I = P(1 + rt)

Example: $5,000 at 6% simple interest for 10 years.

I = 5,000 x 0.06 x 10 = $3,000

Estimated total: $8,000. You earn the same $300 in interest every year.

The compound interest formula

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

Where:

A = estimated future value
P = principal
r = annual interest rate (as a decimal)
n = number of times interest compounds per year
t = time in years

Example: $5,000 at 6% compounded annually for 10 years.

A = 5,000 x (1 + 0.06/1)^(1 x 10) = 5,000 x (1.06)^10

Estimated total: approximately $8,954

The interest earned is approximately $3,954. That is $954 more than simple interest on the same terms. The extra comes from earning interest on interest.

Side-by-side comparison: $5,000 at 6% for 10 years

Year	Simple interest balance	Compound interest balance (annual)
0	$5,000	$5,000
1	$5,300	$5,300
2	$5,600	$5,618
3	$5,900	$5,955
5	$6,500	$6,691
7	$7,100	$7,518
10	$8,000	$8,954

In year 1, both balances are $5,300. The difference is zero because there is no prior interest to compound. By year 10, the compound balance is approximately $954 ahead.

Over 20 years, the gap widens. Simple interest on $5,000 at 6% yields $11,000 total. Compound interest yields approximately $16,036. The compound balance is $5,036 ahead, more than the original principal.

How compounding frequency changes results

More frequent compounding means interest gets added to the balance sooner, so it starts earning its own interest earlier. Here is $5,000 at 6% for 10 years with different frequencies:

Compounding frequency	n	Estimated total
Annually	1	$8,954
Semi-annually	2	$9,031
Quarterly	4	$9,070
Monthly	12	$9,097
Daily	365	$9,110

The jump from annual to monthly compounding adds approximately $143. Going from monthly to daily adds only about $13. Returns diminish as frequency increases. The theoretical maximum is continuous compounding, calculated with the formula A = Pe^(rt), which gives approximately $9,111 here.

The Rule of 72

A quick way to estimate how long it takes for compound interest to double your money:

Years to double = 72 / interest rate

At 6%, your money doubles in approximately 72 / 6 = 12 years. At 8%, approximately 9 years. At 4%, approximately 18 years.

This approximation works well for rates between 2% and 15%. It assumes compound interest; simple interest at 6% takes 16.7 years to double ($5,000 becomes $10,000 after $300/year x 16.67 years).

When each type applies

Simple interest is common in short-term personal loans, auto loans, and some bonds. Compound interest is standard for savings accounts, certificates of deposit, investment returns, and most long-term financial products.

Credit card debt also compounds. A $5,000 credit card balance at 20% APR compounded daily grows to approximately $6,107 after one year if no payments are made. The same balance at simple interest would be $6,000.

Key takeaways

Simple interest formula: I = P x r x t (interest on principal only)
Compound interest formula: A = P(1 + r/n)^(nt) (interest on principal plus prior interest)
On $5,000 at 6% for 10 years, compounding earns approximately $954 more than simple interest
More frequent compounding increases returns, but with diminishing gains past monthly
Rule of 72: divide 72 by the interest rate to estimate years to double with compound interest

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