Simple vs Compound Interest
Simple interest is calculated only on the original principal each period. Compound interest is calculated on the principal plus all previously accumulated interest — so you earn interest on your interest.
Simple Interest
A = P × (1 + r × t)
$10,000 at 8% for 10 years: $10,000 × (1 + 0.8) = $18,000
Compound Interest
A = P × (1 + r/n)^(n×t)
$10,000 at 8% for 10 years (annual): $21,589
The same principal, same rate, same time period — but compounding generates $3,589 more. The gap widens dramatically over longer periods.
The Compound Interest Formula
A = P × (1 + r/n)^(n × t)
A = Final amount (principal + interest)
P = Principal (initial investment)
r = Annual interest rate (as decimal, e.g. 0.08 for 8%)
n = Number of compounding periods per year
t = Time in years
Example: $5,000 at 7% annual rate, compounded monthly, for 15 years
P = 5,000 | r = 0.07 | n = 12 | t = 15
A = 5,000 × (1 + 0.07/12)^(12×15)
A = 5,000 × (1.005833)^180
A = 5,000 × 2.8489 = $14,245
Interest earned: $14,245 − $5,000 = $9,245 — nearly doubling the original investment in earned interest alone.
How Compounding Frequency Affects Returns
The same nominal annual rate produces different results depending on how often it compounds. More frequent compounding = slightly higher effective return:
The difference between annual and daily compounding on $10,000 over 10 years is only $465 — meaningful but not dramatic. The compounding frequency matters far less than the rate and time horizon.
The Rule of 72
The Rule of 72 is a quick mental math shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
Years to double = 72 ÷ annual return rate (%)
4% return → doubles in 18 years
6% return → doubles in 12 years
8% return → doubles in 9 years
10% return → doubles in 7.2 years
12% return → doubles in 6 years
15% return → doubles in 4.8 years
Works in reverse too: if prices double in 18 years (inflation), the implied inflation rate is 72 ÷ 18 = 4% per year.
Time in Market vs. Timing the Market
The most important variable in compound interest is time, not the rate. Consider two investors with the same total contributions:
Alex — starts at 25
Invests $200/month for 10 years (ages 25–35), then stops.
Total contributed: $24,000
At age 65 at 8% return: $349,000
Sam — starts at 35
Invests $200/month for 30 years (ages 35–65).
Total contributed: $72,000
At age 65 at 8% return: $298,000
Alex invested 3× less money but ended up with 17% more — purely because of 10 extra years of compounding. This is the fundamental argument for starting to invest as early as possible.
Compound Interest in Reverse: Debt
Compound interest works against you when you carry debt. A credit card balance of $5,000 at 20% APR, compounded daily, with a minimum payment of $100/month, will take over 9 years to pay off and cost $7,000+ in interest — more than the original balance. The same mathematical force that builds wealth destroys it when you are the borrower. This is why high-interest debt elimination is the highest guaranteed return investment available.