Simple vs Compound Interest Calculator
Simple interest grows linearly — you earn the same dollar amount every year. Compound interest grows exponentially — you earn interest on your interest. This calculator shows exactly how large that gap becomes over time, letting you compare both methods side-by-side with a full year-by-year breakdown. Whether you're evaluating a savings account, a loan, or an investment, knowing the difference can change your decision.
When to use this calculator
- Compare a simple-interest personal loan against a compound-interest savings account
- Estimate how much more a 401(k) earns versus a fixed simple-interest bond over 20–30 years
- Understand why high-rate credit card debt (compounding daily) grows so much faster than stated
- Show students or clients the time-value impact of compounding frequency
- Evaluate whether a simple-interest auto loan beats a compound-interest home equity line
- Project retirement nest-egg growth under different compounding assumptions
How it works
2 min readWhat is compound interest?
Compound interest is interest earned on both the principal and previously accumulated interest, growing exponentially over time. Unlike simple interest, which generates fixed returns annually, compound interest reinvests earnings, causing wealth to accelerate. For example, $10,000 at 7% compounds to $76,123 in 30 years versus $21,000 with simple interest—a $55,123 difference.
Formulas
Simple Interest
Simple interest is calculated only on the original principal:
I = P × r × t
Final Balance = P + IWhere:
Compound Interest
Compound interest is calculated on the principal plus all previously accumulated interest:
A = P × (1 + r/n)^(n×t)Where:
For continuous compounding, the formula uses Euler's number:
A = P × e^(r×t)---
Worked Example
Principal: $10,000 | Rate: 7% | Term: 30 years | Monthly compounding
Simple interest:
Compound interest (monthly):
Compound advantage: $45,123 extra — just from reinvesting interest.
Year-by-Year Snapshot (selected years)
| Year | Simple Balance | Compound Balance (monthly) | Difference |
|---|---|---|---|
| 5 | $13,500 | $14,176 | $676 |
| 10 | $17,000 | $20,097 | $3,097 |
| 20 | $24,000 | $40,388 | $16,388 |
| 30 | $31,000 | $76,123 | $45,123 |
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Key Concept: The Compounding Effect
In year 1, both methods earn nearly the same amount. The gap widens slowly at first, then accelerates dramatically — this is the exponential curve in action. At higher rates or longer terms, the difference becomes even more pronounced.
Compounding frequency also matters: daily compounding yields slightly more than monthly, which yields more than annual. The difference between frequencies narrows as you move from annual → monthly → daily, but the jump from simple to any compounding is always the largest.
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When NOT to Apply These Formulas
Frequently asked questions
What is the main difference between simple and compound interest?
Simple interest is calculated only on the original principal every period. Compound interest is calculated on the principal plus all interest already accumulated, so each period's interest base grows larger. Over time, this causes compound interest to grow exponentially while simple interest grows in a straight line.
Which type of interest is better for a borrower?
Simple interest is better for borrowers. You pay interest only on the outstanding principal, not on accrued interest. Many auto loans and short-term personal loans use simple interest. Credit cards, in contrast, compound daily — which is why carrying a balance is so costly.
Does compounding frequency really matter much?
It matters, but less than most people expect once you move beyond annual compounding. The biggest jump is from annual to monthly. Going from monthly (n=12) to daily (n=365) on $10,000 at 7% for 30 years adds roughly $700 more — about 1% of the total balance. The rate and time period are far more impactful than frequency.
What does 'continuous compounding' mean?
Continuous compounding is the mathematical limit as n approaches infinity, using the formula A = P·e^(rt). It represents interest compounding at every infinitesimally small moment. It produces the maximum possible compound return for a given rate and term. In practice, no financial product compounds truly continuously, but some savings bonds and theoretical finance models use it.
Can I use this calculator for loans as well as savings?
Yes for simple interest loans — the formula I=P·r·t applies directly to the total interest cost. However, for amortizing loans (mortgages, car loans), the compound formula overstates the total interest because payments reduce the principal over time. Use a dedicated amortization calculator for those scenarios.
Why does the compound interest total grow so much faster after year 10?
Because the interest base (principal + accumulated interest) keeps expanding. In early years, accumulated interest is small, so the extra earnings from compounding are modest. By year 15–20, accumulated interest can equal or exceed the original principal, meaning the 'interest on interest' component becomes the dominant source of growth.
What annual rate inputs are realistic?
High-yield savings accounts: 4–5% (2026). Index fund historical average: ~7% real, ~10% nominal. Credit cards: 20–29%. Mortgages: 6–8%. Personal loans: 8–25%. Rates outside 0.1%–30% are unusual; inputs above 50% may indicate an error in the rate field.
Does this account for taxes on interest earned?
No. The calculator shows pre-tax nominal growth. Interest income is generally taxable as ordinary income in the US (IRS Publication 550). For tax-advantaged accounts (401k, IRA, HSA), taxes are deferred or exempt — the compound totals shown represent the actual growth inside those accounts.
How accurate is the year-by-year table?
The yearly snapshots are exact values from the formulas at each integer year, not approximations. For compound interest, the balance at year Y is P·(1+r/n)^(n·Y). For simple interest, it is P·(1+r·Y). No rounding is applied until display.