Interest Calculator
Calculate simple and compound interest side-by-side. Compare how your money grows with different compounding frequencies and interest rates.
Simple Interest
Compound Interest
Understanding APY
Your stated 5% rate with monthly compounding yields an APY (Annual Percentage Yield) of 5.116%. APY represents your actual annual return including the effect of compounding. When comparing savings accounts, always compare APY to APY for accurate results.
Growth Over Time
Compound Interest Breakdown
Year-by-Year Comparison
| Year | Simple Balance | Compound Balance | Difference |
|---|---|---|---|
| 0 | $10,000 | $10,000 | +$0 |
| 1 | $10,500 | $10,512 | +$12 |
| 2 | $11,000 | $11,049 | +$49 |
| 3 | $11,500 | $11,615 | +$115 |
| 4 | $12,000 | $12,209 | +$209 |
| 5 | $12,500 | $12,834 | +$334 |
| 6 | $13,000 | $13,490 | +$490 |
| 7 | $13,500 | $14,180 | +$680 |
| 8 | $14,000 | $14,906 | +$906 |
| 9 | $14,500 | $15,668 | +$1,168 |
| 10 | $15,000 | $16,470 | +$1,470 |
Rule of 72
At 5% compound interest, your money will double in approximately 14.4 years (72 / 5 = 14.4). This quick mental math shortcut helps you evaluate investment opportunities instantly.
Related Calculators
About This Calculator
The Interest Calculator is your essential tool for understanding how money grows through both simple and compound interest. Whether you're evaluating savings accounts, comparing loan offers, or planning long-term investments, this calculator shows you exactly how interest works in both forms side-by-side. Understanding the difference between simple and compound interest is fundamental to making smart financial decisions in 2026's evolving rate environment.
Simple interest calculates returns only on your original principal, creating predictable linear growth. Compound interest, often called "the eighth wonder of the world," calculates returns on your principal plus accumulated interest, creating exponential growth that accelerates over time. This calculator lets you compare both methods simultaneously, showing how compounding frequency affects your final balance and helping you understand why a 5% compound interest rate actually yields more than 5% annually through the power of APY.
With the Federal Reserve adjusting rates throughout 2025-2026, understanding interest calculations has never been more important. High-yield savings accounts now offer 4.5-5.25% APY, while the prime rate stands at 8.5% as of January 2026. Use this calculator to model different scenarios, compare investment options, and see firsthand why Einstein allegedly called compound interest the most powerful force in the universe.
Trusted Sources
How to Use the Interest Calculator
- 1Enter your principal amount - this is the starting sum you are investing or borrowing. Even modest amounts like $1,000 can demonstrate the power of compounding over time.
- 2Input your annual interest rate as a percentage. For reference: high-yield savings accounts offer 4.5-5.25% APY in 2026, while the average savings account pays just 0.45%. Investment returns historically average 7-10% for diversified stock portfolios.
- 3Set your time period in years. The longer the duration, the more dramatic the difference between simple and compound interest becomes. Try periods of 5, 10, 20, and 30 years to see exponential growth.
- 4Select your compounding frequency from the dropdown: annually, semi-annually, quarterly, monthly, or daily. More frequent compounding yields higher returns - daily compounding on a 5% rate produces a 5.13% APY.
- 5Review your results showing both simple interest and compound interest calculations side-by-side. See the interest earned, final amount, and the APY (Annual Percentage Yield) for compound interest.
- 6Examine the growth chart to visualize how compound interest accelerates over time compared to the linear growth of simple interest.
- 7Experiment with different scenarios by adjusting inputs to understand how small changes in rate or time dramatically affect outcomes.
Formula
Simple: I = P x R x T | Compound: A = P(1 + r/n)^(nt)Two fundamental formulas govern interest calculations. Simple interest uses I = P x R x T, where I is interest earned, P is principal, R is the annual rate as a decimal, and T is time in years. This creates linear growth - at 5%, $10,000 earns exactly $500 every year. Compound interest uses A = P(1 + r/n)^(nt), where A is the final amount, P is principal, r is annual rate as a decimal, n is compounding frequency per year, and t is time in years. This creates exponential growth because you earn interest on your interest. At 5% compounded monthly, $10,000 earns $512.67 in year one, but $538.33 in year two as your balance grows. The difference compounds dramatically over time: $10,000 at 5% for 30 years yields $15,000 with simple interest but $43,219 with monthly compound interest - nearly triple the amount.
Simple vs Compound Interest: The Fundamental Difference
Understanding the core difference between simple and compound interest is essential for every financial decision you make, from choosing savings accounts to evaluating loan offers.
Simple Interest: Linear Growth
Simple interest calculates earnings only on your original principal. The formula is straightforward:
Interest = Principal x Rate x Time
I = P x R x T
Example: $10,000 at 6% simple interest for 5 years:
- Year 1: $10,000 x 0.06 x 1 = $600 interest
- Year 2: $10,000 x 0.06 x 1 = $600 interest
- Year 3: $10,000 x 0.06 x 1 = $600 interest
- Total after 5 years: $13,000 ($3,000 total interest)
Each year earns exactly the same interest because calculations are always based on the original $10,000.
Compound Interest: Exponential Growth
Compound interest calculates earnings on your principal PLUS accumulated interest:
Final Amount = Principal x (1 + Rate/n)^(n x Time)
A = P(1 + r/n)^(nt)
Example: $10,000 at 6% compound interest (annual compounding) for 5 years:
- Year 1: $10,000 x 1.06 = $10,600 (earned $600)
- Year 2: $10,600 x 1.06 = $11,236 (earned $636)
- Year 3: $11,236 x 1.06 = $11,910 (earned $674)
- Year 4: $11,910 x 1.06 = $12,625 (earned $715)
- Year 5: $12,625 x 1.06 = $13,382 (earned $757)
- Total after 5 years: $13,382 ($3,382 total interest)
Notice how interest earned increases each year. That extra $382 over simple interest seems small over 5 years, but the difference explodes over longer periods.
Long-Term Comparison: $10,000 at 6%
| Years | Simple Interest | Compound (Monthly) | Difference |
|---|---|---|---|
| 5 | $13,000 | $13,489 | +$489 |
| 10 | $16,000 | $18,194 | +$2,194 |
| 20 | $22,000 | $33,102 | +$11,102 |
| 30 | $28,000 | $60,226 | +$32,226 |
| 40 | $34,000 | $109,565 | +$75,565 |
After 40 years, compound interest earns 3.2x more than simple interest on identical terms.
How Compounding Frequency Affects Your Returns
The frequency of compounding - how often interest is calculated and added to your balance - has a measurable impact on your final returns. More frequent compounding means your interest starts earning interest sooner.
Compounding Frequency Options:
| Frequency | Times/Year | Description |
|---|---|---|
| Annually | 1 | Once per year |
| Semi-Annually | 2 | Twice per year |
| Quarterly | 4 | Four times per year |
| Monthly | 12 | Twelve times per year |
| Daily | 365 | Every day |
| Continuously | Infinite | Mathematical limit |
Real Impact: $10,000 at 5% for 10 Years
| Compounding | Final Balance | Interest Earned | APY |
|---|---|---|---|
| Simple (none) | $15,000.00 | $5,000.00 | 5.00% |
| Annually | $16,288.95 | $6,288.95 | 5.00% |
| Semi-Annually | $16,386.16 | $6,386.16 | 5.06% |
| Quarterly | $16,436.19 | $6,436.19 | 5.09% |
| Monthly | $16,470.09 | $6,470.09 | 5.12% |
| Daily | $16,486.65 | $6,486.65 | 5.13% |
| Continuously | $16,487.21 | $6,487.21 | 5.13% |
Key Insights:
- Annual vs Monthly: The jump from annual to monthly compounding adds $181 in interest over 10 years
- Monthly vs Daily: Only $16.56 difference - monthly compounding captures most of the benefit
- Daily vs Continuous: Practically identical - daily compounding is mathematically sufficient
- APY Reveals True Yield: A 5% rate compounded monthly is actually 5.12% APY
Why This Matters:
- Savings Accounts: Always compare APY, not stated interest rate
- Credit Cards: Daily compounding works against you on debt (average 22.76% APR = 25.34% APY)
- Investments: Dividend reinvestment creates compound growth even in stocks
- Mortgages: Most use monthly compounding on the remaining balance
The Continuous Compounding Formula:
For the mathematically curious, continuous compounding uses Euler's number (e ≈ 2.71828):
A = P x e^(rt)
This represents the theoretical maximum growth at any given interest rate, though in practice daily compounding achieves 99.99% of this maximum.
2026 Interest Rate Environment
Understanding current market rates helps you evaluate whether an offer is competitive and set realistic expectations for your investments and borrowing costs.
2026 Federal Reserve and Benchmark Rates (January 2026):
| Rate Type | Current Rate | One Year Ago | Notes |
|---|---|---|---|
| Federal Funds Rate | 4.25-4.50% | 5.25-5.50% | Fed's target overnight rate |
| Prime Rate | 8.50% | 9.50% | Base rate for many loans |
| 10-Year Treasury | 4.15% | 4.40% | Key mortgage benchmark |
| 30-Year Mortgage | 6.45% | 6.85% | Average conforming rate |
| SOFR | 4.30% | 5.33% | Replaced LIBOR in 2024 |
Consumer Savings Rates (January 2026):
| Account Type | Average Rate | Best Available | Notes |
|---|---|---|---|
| Regular Savings | 0.45% APY | - | National average |
| High-Yield Savings | 4.50-5.25% APY | 5.25% | Online banks |
| Money Market | 4.25-5.00% APY | 5.00% | Minimum balance required |
| 1-Year CD | 4.50-5.10% APY | 5.10% | Early withdrawal penalty |
| 5-Year CD | 4.00-4.75% APY | 4.75% | Rate lock for 5 years |
Loan Interest Rates (January 2026):
| Loan Type | Average Rate | Rate Range | Notes |
|---|---|---|---|
| 30-Year Fixed Mortgage | 6.45% | 6.00-7.25% | Varies by credit score |
| 15-Year Fixed Mortgage | 5.75% | 5.25-6.50% | Lower rate, higher payment |
| Auto Loan (New) | 7.25% | 5.50-12.00% | 60-month term typical |
| Auto Loan (Used) | 8.50% | 6.50-14.00% | Higher risk for lenders |
| Personal Loan | 12.50% | 8.00-36.00% | Unsecured borrowing |
| Credit Card | 22.76% | 15.00-30.00% | Variable, compounds daily |
Investment Return Expectations:
| Asset Class | Historical Average | 2026 Outlook | Notes |
|---|---|---|---|
| S&P 500 Index | 10.0% | 7-9% | Nominal returns |
| Total Stock Market | 10.2% | 7-9% | Broad diversification |
| Bond Aggregate | 5.5% | 4-6% | Interest rate sensitive |
| 60/40 Portfolio | 8.5% | 6-8% | Classic allocation |
| Real Estate (REITs) | 9.5% | 6-10% | Income + appreciation |
| High-Yield Bonds | 7.5% | 6-8% | Higher risk |
Key Takeaways for 2026:
- Savings: High-yield accounts pay 10x the national average - don't leave money in traditional savings
- Mortgages: Rates have declined from 2024 peaks but remain above pre-pandemic levels
- Credit Cards: Average APR over 22% makes carrying a balance extremely expensive
- Investments: Expect moderate returns; bonds competitive with stocks on risk-adjusted basis
The Rule of 72: Quick Mental Math for Doubling Time
The Rule of 72 is a powerful mental math shortcut that every investor should know. It quickly estimates how long it takes for money to double at a given compound interest rate.
The Rule of 72 Formula:
Years to Double = 72 / Interest Rate
Quick Reference Table:
| Interest Rate | Years to Double | After 36 Years |
|---|---|---|
| 2% | 36 years | 2x original |
| 3% | 24 years | 2.8x original |
| 4% | 18 years | 4x original |
| 6% | 12 years | 8x original |
| 8% | 9 years | 16x original |
| 10% | 7.2 years | 32x original |
| 12% | 6 years | 64x original |
Practical Applications:
1. Inflation Impact: At 3% inflation, your money's purchasing power halves in 24 years (72 / 3 = 24). A dollar today buys only 50 cents worth in 2050.
2. Savings Account Reality Check: At 0.45% (national average), money doubles in 160 years (72 / 0.45 = 160). At 5% high-yield savings, it doubles in 14.4 years.
3. Investment Planning: At 7% after-inflation returns, investments double every 10.3 years:
- Age 25 to 35: $10,000 becomes $20,000
- Age 35 to 45: $20,000 becomes $40,000
- Age 45 to 55: $40,000 becomes $80,000
- Age 55 to 65: $80,000 becomes $160,000
4. Debt Danger: At 22.76% credit card interest, debt doubles in just 3.2 years if unpaid.
Variations of the Rule:
Rule of 114 (Triple Your Money):
Years to Triple = 114 / Interest Rate
At 8%: 114 / 8 = 14.25 years to triple
Rule of 144 (Quadruple Your Money):
Years to Quadruple = 144 / Interest Rate
At 8%: 144 / 8 = 18 years to quadruple
Why Does 72 Work?
The Rule of 72 is derived from the natural logarithm of 2 (approximately 0.693), which relates to doubling. The number 72 is used because it's easily divisible by many common interest rates (2, 3, 4, 6, 8, 9, 12) and provides accuracy within 1-2% for rates between 4% and 12%.
Accuracy Comparison:
| Rate | Rule of 72 | Exact Years | Error |
|---|---|---|---|
| 4% | 18.0 years | 17.67 years | +1.9% |
| 6% | 12.0 years | 11.90 years | +0.8% |
| 8% | 9.0 years | 9.01 years | -0.1% |
| 10% | 7.2 years | 7.27 years | -1.0% |
| 12% | 6.0 years | 6.12 years | -2.0% |
APR vs APY: Understanding the Real Cost and Yield
APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are both ways to express interest rates, but they tell different stories. Understanding this distinction is crucial for comparing financial products accurately.
Definitions:
APR (Annual Percentage Rate):
- The simple interest rate without compounding
- Used for loans, credit cards, mortgages
- Does NOT include the effect of compounding within the year
- May or may not include fees (depends on product)
APY (Annual Percentage Yield):
- The effective annual rate INCLUDING compounding
- Used for savings accounts, CDs, investments
- Shows your actual yearly return
- Always higher than APR when compounding occurs
The Conversion Formula:
APY = (1 + APR/n)^n - 1
Where n = number of compounding periods per year
APR to APY Conversion Table:
| APR | Monthly Compounding APY | Daily Compounding APY |
|---|---|---|
| 3.00% | 3.04% | 3.05% |
| 4.00% | 4.07% | 4.08% |
| 5.00% | 5.12% | 5.13% |
| 6.00% | 6.17% | 6.18% |
| 8.00% | 8.30% | 8.33% |
| 10.00% | 10.47% | 10.52% |
| 20.00% | 21.94% | 22.13% |
Real-World Examples:
Savings Account:
- Bank A advertises 4.90% APR, compounded monthly
- Bank B advertises 5.00% APY
- Which is better?
Bank A: APY = (1 + 0.049/12)^12 - 1 = 5.01% APY Bank A is actually better despite the lower advertised number!
Credit Card:
- 22.99% APR, compounded daily
- APY = (1 + 0.2299/365)^365 - 1 = 25.83% APY
- You're paying 25.83% effective interest on carried balances
Why Banks Use Different Terms:
- Savings products advertise APY because the higher number is more attractive
- Loan products advertise APR because the lower number seems more affordable
- Regulations require APR disclosure on loans and APY on deposits
Critical Comparison Tips:
- When comparing savings accounts: Compare APY to APY
- When comparing loans: Compare APR to APR, but check if fees are included
- For credit cards: The APR advertised daily compounds to much higher effective rates
- For mortgages: APR should include points and fees; compare APR not just the interest rate
The True Cost of Credit Card Interest:
| Advertised APR | Daily Compounding APY | Extra Cost vs APR |
|---|---|---|
| 18.99% | 20.90% | +1.91% |
| 22.99% | 25.83% | +2.84% |
| 26.99% | 30.88% | +3.89% |
| 29.99% | 34.96% | +4.97% |
A "22.99% APR" credit card actually charges you 25.83% annualized interest on carried balances.
Interest Calculation Examples and Practice Problems
Let's work through practical examples to solidify your understanding of both simple and compound interest calculations.
Example 1: Savings Account Comparison
You have $25,000 to deposit. Compare two options over 5 years:
- Option A: 4.75% APY high-yield savings (compounds daily)
- Option B: 4.50% simple interest CD (interest paid at maturity)
Option A (Compound): A = $25,000 x (1 + 0.0475/365)^(365 x 5) A = $25,000 x 1.2676 A = $31,690
Interest earned: $6,690
Option B (Simple): I = $25,000 x 0.045 x 5 I = $5,625
Total: $30,625
Difference: $1,065 more with compound interest (Option A wins despite lower stated rate because of compounding)
Example 2: Auto Loan (Simple Interest)
$35,000 auto loan at 7.25% simple interest for 60 months:
Monthly payment calculation requires amortization, but total interest: I = $35,000 x 0.0725 x 5 = $12,687.50
With compound interest at the same rate: A = $35,000 x (1.0725)^5 = $49,602 Interest = $14,602
Simple interest saves $1,914.50 - this is why simple interest auto loans benefit borrowers.
Example 3: Rule of 72 Verification
Does $50,000 at 8% actually double in 9 years (72/8)?
Using compound interest (annual): A = $50,000 x (1.08)^9 = $99,950
Yes! It reaches $99,950, essentially double.
Example 4: Monthly Contributions
Start with $5,000, add $200/month at 6% for 20 years:
Future value of initial investment: FV = $5,000 x (1.005)^240 = $16,386
Future value of monthly contributions: FV = $200 x [(1.005)^240 - 1] / 0.005 = $92,408
Total: $108,794
- Total contributed: $5,000 + ($200 x 240) = $53,000
- Interest earned: $55,794 (105% return on contributions!)
Example 5: Finding the Required Rate
You want $100,000 in 15 years, starting with $40,000. What rate do you need?
Rearranging: r = (A/P)^(1/t) - 1 r = ($100,000/$40,000)^(1/15) - 1 r = (2.5)^0.0667 - 1 r = 0.0627 = 6.27% annual return needed
Example 6: Time to Reach a Goal
How long until $10,000 becomes $50,000 at 7% compound interest?
Rearranging: t = ln(A/P) / ln(1+r) t = ln(5) / ln(1.07) t = 1.609 / 0.0677 t = 23.8 years
Rule of 72 check: To 5x, need to double 2.32 times. 72/7 = 10.3 years to double, so 10.3 x 2.32 = 23.9 years. Confirmed!
Jar Insight: The Fascinating History of Interest
The Ancient Origins of Interest Calculations:
Interest has been charged on loans for over 4,000 years, making it one of humanity's oldest financial concepts.
Babylon (2000 BCE): The Code of Hammurabi established the first known interest rate regulations. Maximum rates were 20% per year on silver loans and 33.3% on grain loans. These were simple interest calculations - compound interest hadn't been invented yet. Babylonians used a base-60 number system, which is why we still have 60 seconds per minute.
Ancient Rome: Romans charged "usura" (interest) typically between 4-12% annually. The word "usury" originally just meant interest but later came to mean excessive interest. Julius Caesar capped rates at 12% to prevent exploitation.
Medieval Europe: The Catholic Church banned interest (usury) for centuries, considering it sinful to profit from lending money. This led to creative workarounds and the rise of Jewish moneylenders who weren't bound by Church law. Interest was eventually reintroduced as "compensation for the lender's risk."
The Discovery of Compound Interest:
Jacob Bernoulli (1655-1705) made a groundbreaking discovery while studying compound interest. He asked: "What happens if we compound infinitely often?" His investigation led to the discovery of the mathematical constant e (approximately 2.71828), which is fundamental to continuous compounding and appears throughout mathematics and science.
Benjamin Franklin's Compound Interest Experiment:
In 1790, Benjamin Franklin left 1,000 pounds (about $4,400) each to Boston and Philadelphia in his will, with instructions to invest the money for 200 years. By 1990:
- Boston's fund grew to $5 million
- Philadelphia's fund reached $2 million
This real-world demonstration of compound interest over two centuries showed its remarkable power - and also the impact of different investment choices and management.
The Einstein Quote That Never Was:
Albert Einstein is often credited with calling compound interest "the eighth wonder of the world" or "the most powerful force in the universe." However, there's no evidence he ever said this. The first recorded attribution appeared in 1983, nearly 30 years after Einstein's death. The quotes were likely invented by financial marketers.
What IS True: The mathematics of compound interest is genuinely powerful. An investment doubling every 10 years will multiply 1,024x over 100 years ($1,000 becomes over $1 million).
Pro Tips
- 💡Always compare APY to APY when evaluating savings accounts - a 4.90% rate compounded daily may beat a 5.00% rate compounded annually.
- 💡Use the Rule of 72 for quick mental math: divide 72 by your interest rate to estimate years to double your money.
- 💡High-yield savings accounts pay 4.5-5.25% APY in 2026, compared to 0.45% national average - that is a 10x difference on your emergency fund.
- 💡Credit card interest compounds daily, turning a 22.99% APR into 25.83% effective annual rate - pay balances in full monthly.
- 💡The difference between simple and compound interest grows dramatically over time: $10,000 at 6% for 30 years yields $28,000 (simple) vs $60,226 (compound monthly).
- 💡For loans, simple interest benefits borrowers; for savings, compound interest benefits savers - know which type applies to your accounts.
- 💡Start early: at 7% returns, $10,000 invested at age 25 becomes $160,000 by age 65, while the same investment at age 35 only reaches $80,000.
- 💡Consider inflation when calculating real returns: 5% APY minus 3% inflation equals only 2% real growth in purchasing power.
- 💡Monthly compounding captures most of the benefit - going from monthly to daily adds minimal extra return compared to annual to monthly.
- 💡Paying off high-interest debt (like credit cards at 23%) is equivalent to earning a guaranteed 23% return - prioritize this over investing.
Frequently Asked Questions
Simple interest is calculated only on your original principal amount. If you invest $10,000 at 5% simple interest, you earn exactly $500 per year, every year, regardless of how long you invest. Compound interest is calculated on your principal PLUS any accumulated interest. That same $10,000 at 5% compound interest earns $500 in year one, but $525 in year two (5% of $10,500), $551 in year three, and so on. Over 30 years, $10,000 at 5% simple interest becomes $25,000, while compound interest (monthly compounding) grows to $44,677 - nearly double the simple interest amount.
