Simple vs Compound Interest: Explained with Examples
Simple interest is calculated only on the original principal amount. Compound interest is calculated on the principal plus all previously accumulated interest — often called “interest on interest.” This single difference creates an enormous gap over time: $10,000 invested at 5% for 30 years grows to $25,000 with simple interest but $43,219 with compound interest(annual compounding) — a difference of $18,219 from the same starting amount and rate.
Quick Answer
- *Simple interest formula: I = P × r × t (interest grows linearly).
- *Compound interest formula: A = P(1 + r/n)^(nt) (interest grows exponentially).
- *Over 30 years at 5%, compound interest earns 73% more than simple interest on the same principal.
- *According to the SEC, the S&P 500 has averaged roughly 10% annual returns historically, making compounding the primary driver of long-term investment growth.
Simple Interest: Formula and Examples
Simple interest is the most straightforward form of interest. You earn (or pay) interest only on the original principal — the amount never changes.
Simple Interest Formula
I = P × r × t
- I = Interest earned
- P = Principal (initial amount)
- r = Annual interest rate (as a decimal)
- t = Time in years
Example 1: Simple Interest on a Savings Deposit
You deposit $5,000 at 6% simple interest for 3 years:
- Year 1: $5,000 × 0.06 = $300
- Year 2: $5,000 × 0.06 = $300
- Year 3: $5,000 × 0.06 = $300
- Total interest: $900
- Total value: $5,900
Notice that the interest is the same every year — $300 — because it is always calculated on the original $5,000.
Example 2: Simple Interest on a Car Loan
You borrow $20,000 for a car at 5% simple interest for 5 years:
I = $20,000 × 0.05 × 5 = $5,000 in total interest
Total repayment: $25,000
Monthly payment: $25,000 ÷ 60 months = $416.67
Compound Interest: Formula and Examples
Compound interest calculates interest on the principal and on all previously earned interest. This creates exponential growth over time.
Compound Interest Formula
A = P(1 + r/n)nt
- A = Final amount
- P = Principal
- r = Annual interest rate (decimal)
- n = Number of times compounded per year
- t = Time in years
Example 3: Compound Interest on a Savings Account
You deposit $5,000 at 6% compounded annually for 3 years:
- Year 1: $5,000 × 1.06 = $5,300 (interest: $300)
- Year 2: $5,300 × 1.06 = $5,618 (interest: $318)
- Year 3: $5,618 × 1.06 = $5,955.08 (interest: $337.08)
- Total interest: $955.08
- Total value: $5,955.08
Compare this to $5,900 with simple interest — compound interest earned $55.08 more in just 3 years. The gap widens dramatically over longer time horizons.
Side-by-Side Comparison: $10,000 at 5%
Here is how $10,000 grows at 5% under both methods, with compound interest calculated annually:
| Year | Simple Interest | Compound Interest | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,500 | $0 |
| 5 | $12,500 | $12,763 | $263 |
| 10 | $15,000 | $16,289 | $1,289 |
| 15 | $17,500 | $20,789 | $3,289 |
| 20 | $20,000 | $26,533 | $6,533 |
| 25 | $22,500 | $33,864 | $11,364 |
| 30 | $25,000 | $43,219 | $18,219 |
After 30 years, compound interest has earned 73% more than simple interest. At year 1, there is zero difference. By year 10, the gap is $1,289. By year 30, it is $18,219. This accelerating gap is the essence of exponential growth.
How Compounding Frequency Affects Growth
The more frequently interest compounds, the more you earn. Here is $10,000 at 5% for 10 years with different compounding frequencies:
| Compounding Frequency | n (times/year) | Value After 10 Years | Total Interest |
|---|---|---|---|
| Annually | 1 | $16,289 | $6,289 |
| Semi-annually | 2 | $16,386 | $6,386 |
| Quarterly | 4 | $16,436 | $6,436 |
| Monthly | 12 | $16,470 | $6,470 |
| Daily | 365 | $16,487 | $6,487 |
Moving from annual to daily compounding adds $198 over 10 years on a $10,000 deposit. The difference is more significant at higher rates and larger balances.
Where Each Type of Interest Is Used
| Product | Interest Type | Why |
|---|---|---|
| Savings accounts | Compound (daily) | Benefits the depositor |
| CDs | Compound (daily/monthly) | Benefits the depositor |
| Credit cards | Compound (daily) | Benefits the issuer (costs the borrower more) |
| Mortgages | Compound (monthly) | Standard amortized loan |
| Auto loans | Simple | Interest based on remaining principal |
| Student loans (federal) | Simple | Interest does not compound while in school |
| Personal loans | Simple or compound | Varies by lender |
| Bonds | Compound (semi-annual) | Standard coupon reinvestment |
The Rule of 72: Quick Doubling Estimate
The Rule of 72 provides a quick estimate of how long it takes to double your money with compound interest:
Years to Double = 72 ÷ Interest Rate
- At 4%: 72 ÷ 4 = 18 years
- At 6%: 72 ÷ 6 = 12 years
- At 8%: 72 ÷ 8 = 9 years
- At 10%: 72 ÷ 10 = 7.2 years
With simple interest, your money never truly “doubles” through the same exponential mechanics. At 5% simple interest, it takes 20 years to double ($10,000 to $20,000). With 5% compound interest, it takes only 14.4 years — nearly 6 years faster.
See the difference for your own numbers
Use our free Interest Calculator →Also useful: Compound Interest Calculator · Savings Calculator
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all accumulated interest. Over 30 years at 5%, $10,000 grows to $25,000 with simple interest but $43,219 with compound interest — a 73% difference.
Which is better: simple or compound interest?
For savers and investors, compound interest is better because your money grows faster. For borrowers, simple interest is better because you pay less total interest. Savings accounts use compound interest; some auto loans and student loans use simple interest.
How do you calculate simple interest?
Use the formula I = P × r × t. For example, $5,000 at 6% for 3 years: I = $5,000 × 0.06 × 3 = $900 in interest. The total after 3 years is $5,900. The interest is the same every year ($300) because it is always based on the original principal.
How often does compound interest compound?
It depends on the product. Savings accounts typically compound daily, CDs compound daily or monthly, bonds compound semi-annually, and credit cards compound daily. More frequent compounding produces slightly more growth — daily vs. annual compounding on $10,000 at 5% yields an extra $198 over 10 years.