Same interest rate. Same time period. Simple interest grows linearly. Compound interest grows exponentially. The difference between the two is the entire reason wealth accumulates.
⏱ 7 min read📊 Side-by-side comparisons🧮 Visual growth tables
The Formulas: Simple vs Compound
Simple Interest:
FV = PV × (1 + r × t)
Where:
FV = Future Value
PV = Principal (initial amount)
r = Interest rate (annual)
t = Time (in years)
Key: Interest only on the principal.
Compound Interest:
FV = PV × (1 + r)^t
Where:
FV = Future Value
PV = Principal
r = Interest rate (annual)
t = Time (in years)
Key: Interest on principal AND all accumulated interest.
The Critical Difference
Simple: You earn interest only on what you started with. Compound: You earn interest on your interest. Your interest earns interest.
This small difference in math creates massively different outcomes over time.
Real Comparison: $10,000 at 7% for 30 Years
Direct ComparisonSimple Interest vs Compound Interest
💡 Difference: $45,123! The same $10,000, same 7% rate, same 30 years. Compound earns you an extra $45,000. Simple interest grows in a straight line. Compound interest curves upward exponentially.
Year-by-Year Breakdown: Where Compound Explodes
Timeline$10,000 at 7%: Simple vs Compound Growth
Year
Simple Interest
Compound Interest
Difference
0
$10,000
$10,000
$0
5
$13,500
$14,026
+$526
10
$17,000
$19,672
+$2,672
15
$20,500
$27,590
+$7,090
20
$24,000
$38,697
+$14,697
25
$27,500
$54,274
+$26,774
30
$31,000
$76,123
+$45,123
💡 The first 10 years: compound is $2,672 ahead. By year 25, it's $26,774 ahead. By year 30, it's $45,123 ahead. The gap accelerates because the interest is compounding on a growing base.
Why Compound Interest Accelerates Over Time
Annual InterestHow Much Interest You Earn Each Year
Year
Simple (Constant)
Compound (Growing)
Year 1
+$700 (7% of $10K)
+$700 (7% of $10K)
Year 5
+$700 (7% of $10K)
+$977 (7% of $13,960)
Year 10
+$700 (7% of $10K)
+$1,377 (7% of $19,672)
Year 20
+$700 (7% of $10K)
+$2,709 (7% of $38,697)
Year 30
+$700 (7% of $10K)
+$5,328 (7% of $76,123)
💡 Simple interest earns you a flat $700 every year (boring). Compound interest earns you more each year because the base keeps growing. Year 30's interest ($5,328) is 7.6x the first year's interest. This is exponential growth.
Different Compounding Frequencies
Interest can compound annually, quarterly, monthly, or even daily. More frequent compounding = faster growth.
Comparison$5,000 at 5% APR, 10 Years, Different Frequencies
Compounding Frequency
Formula
Final Value
Interest Earned
Annual (n=1)
5000 × (1.05)^10
$8,144
$3,144
Quarterly (n=4)
5000 × (1+0.05/4)^40
$8,208
$3,208
Monthly (n=12)
5000 × (1+0.05/12)^120
$8,235
$3,235
Daily (n=365)
5000 × (1+0.05/365)^3650
$8,253
$3,253
Continuous
5000 × e^(0.05×10)
$8,259
$3,259
💡 Daily compounding earns $109 more than annual compounding. It's not dramatic for small amounts and short periods, but over 30 years with larger balances, daily compounding becomes significant.
Simple Interest: Where It's Actually Used
Simple interest still exists—mostly in loans and bonds.
Real UseSimple Interest in Practice
Bond coupon payments: A $10,000 bond with 5% coupon pays you $500/year, always. No compounding on that $500 unless you reinvest it.
Car loans: Often calculated with simple interest (or a variation). The monthly payment is fixed, and you're paying down principal + accrued interest.
Savings account without interest reinvestment: If you withdraw interest every month instead of letting it compound, you're earning simple interest.
💡 Simple interest is transparent and predictable, but it builds wealth slowly. For personal savings and investments, you want compound interest. For loans, simple interest is preferable (lower costs).
The Rule of 72 Connection
The Rule of 72 is actually the Rule of Compounding. It only works because interest compounds.
How Rule of 72 Proves Compounding Power
At 7% interest, your money doubles in 72 ÷ 7 = 10.3 years.
With simple interest, doubling takes 100 ÷ 7 = 14.3 years.
Compound interest doubles your money 4 years faster. Over 30 years, you don't get just 2x your money—you get 7.6x. This exponential multiplier is why compounding is called the "eighth wonder of the world."
Practice: Calculate Simple vs Compound
🏆 Problem 1 — Student Loan Interest
You borrow $25,000 for college at 6% simple interest, repaid over 10 years. How much total interest do you pay?
Difference: $13,066 extra from compounding. Same rate, same time, but compounding is 32.6% better.
The Compound Interest Principle
For savings and investing: Always choose compound interest. Let your interest earn interest. Don't withdraw it. For borrowing: Simple interest is cheaper, but most loans use compound or amortization (worse). Over time: Compound interest is the force that turns $10,000 into $100,000+. It's not magic. It's math.