This interest calculator handles both simple and compound interest, so you can compare the two side by side. Enter the principal, annual rate, and time in years; for compound interest, choose how often interest is added to the balance.
The difference between the two methods grows with time. Simple interest pays the same dollar amount every year, while compound interest pays interest on interest, producing exponential growth. Over a few months the gap is trivial; over decades it becomes enormous — which is why savings accounts, credit cards, and investments all use compounding.
Simple vs. Compound Interest Formulas
Simple interest is calculated only on the original principal:
I = P × r × t
Where I is interest, P is principal, r is the annual rate as a decimal, and t is time in years. The final amount is A = P + I = P(1 + rt).
Compound interest adds each period’s interest to the balance, so future interest is earned on a growing base:
A = P(1 + r/n)^(nt)
Where n is the number of compounding periods per year (1 annually, 4 quarterly, 12 monthly, 365 daily). Compound interest earned is A − P. For identical inputs, compound interest always yields more than simple interest whenever t exceeds one compounding period.
Where Each Type Is Used
Knowing which method applies helps you read loan and savings terms correctly:
- Simple interest: most auto loans, many personal loans, Treasury bills, and short-term promissory notes. Interest accrues daily on the current principal but never compounds.
- Compound interest: savings accounts, CDs, money market accounts, credit cards (usually daily compounding), mortgages, and investment returns.
- Federal student loans use simple daily interest, but unpaid interest can capitalize (get added to principal) after deferment — a one-time compounding event.
- For borrowers, simple interest is cheaper; for savers, more frequent compounding is better.
Example: $5,000 at 5% for 5 Years, Both Ways
Simple interest: I = 5,000 × 0.05 × 5 = $1,250, for a final amount of $6,250. Each year earns exactly $250, no matter how large the balance grows.
Compound interest (annual): A = 5,000 × (1.05)^5 = $6,381.41, so interest earned is $1,381.41 — $131.41 more than simple interest, because each year’s interest joins the principal.
Compound interest (monthly): A = 5,000 × (1 + 0.05/12)^60 = $6,416.79, earning $1,416.79. Stretch the term to 20 years and the gap widens dramatically: $5,000 simple versus $8,266 compounded annually.
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal (I = Prt), so it grows linearly. Compound interest is calculated on principal plus previously earned interest (A = P(1 + r/n)^nt), so it grows exponentially. Given the same rate and time, compounding always produces more interest.
How do I calculate simple interest?
Multiply principal × annual rate × time in years. For example, $5,000 at 5% for 3 years earns 5,000 × 0.05 × 3 = $750. If time is given in months, divide by 12 first: 18 months is t = 1.5.
Do banks use simple or compound interest?
Savings accounts, CDs, and money market accounts use compound interest, typically compounded daily or monthly and credited monthly. Most auto loans and many personal loans use simple daily interest on the remaining principal. Credit cards compound interest daily, which makes carried balances expensive.
How much more does compound interest earn than simple interest?
It depends on rate and time. At 5% for 5 years on $5,000, compounding annually earns $131 more than simple interest. At 5% for 20 years, the gap grows to about $3,266 — compound growth accelerates while simple interest stays flat at $250 per year.
What does compounding frequency mean?
It is how often earned interest is added to the balance — annually, quarterly, monthly, or daily. More frequent compounding earns slightly more: $5,000 at 5% for 5 years yields $6,381 compounded annually versus $6,420 compounded daily, a difference of about $38.