How Compound Interest Works (With Examples)
You put $1,000 in a savings account. After 10 years, it becomes $1,629. That extra $629 came from compound interest. Here is how it works.
Quick Answer
Compound interest earns interest on your interest. $1,000 at 5% for 10 years becomes $1,629 with compounding vs $1,500 with simple interest. Use the free calculator at dotsapps.com to see your numbers.
Simple Interest vs Compound Interest
Simple interest earns interest only on the original amount. $1,000 at 5% earns $50 every year. After 10 years: $1,500.
Compound interest earns interest on the original amount PLUS all the interest earned so far. Year 1: $50. Year 2: $52.50 (5% of $1,050). Year 3: $55.13. It snowballs.
After 10 years with compound interest: $1,628.89. That is $128.89 more than simple interest. The gap gets much bigger over longer periods.
The Compound Interest Formula
The formula is:
A = P × (1 + r/n)^(n×t)
- A = Final amount
- P = Starting amount (principal)
- r = Annual interest rate (as a decimal)
- n = Number of times interest compounds per year
- t = Number of years
Example: $5,000 at 6% compounded monthly for 20 years. A = 5000 × (1 + 0.06/12)^(12×20) = $16,310.19. Your money more than tripled.
Monthly Contributions Make a Huge Difference
Starting with $1,000 is good. Adding $100 per month is game-changing.
$1,000 starting balance + $100/month at 7% for 30 years:
- Total contributed: $37,000
- Final value: $122,709
- Interest earned: $85,709
More than double your money came from compound interest alone. This is why financial advisors tell you to start investing early. Time is the most powerful ingredient.
The Rule of 72: Quick Doubling Estimate
Want to know how long it takes your money to double? Divide 72 by your interest rate.
- 3% rate → 72 ÷ 3 = 24 years to double
- 5% rate → 72 ÷ 5 = 14.4 years to double
- 7% rate → 72 ÷ 7 = 10.3 years to double
- 10% rate → 72 ÷ 10 = 7.2 years to double
This rule is a rough estimate, but it is surprisingly accurate. Great for quick mental math when comparing investment options.
How to Do It: Step-by-Step
- 1
Open the Compound Interest Calculator at dotsapps.com
- 2
Enter your starting balance (principal)
- 3
Set the annual interest rate
- 4
Add monthly contributions if applicable
- 5
See the year-by-year breakdown of how your money grows
Frequently Asked Questions
How often should interest compound?
More frequent compounding means slightly more growth. Monthly compounding is standard for savings accounts. Daily compounding adds a tiny bit more. The difference between monthly and daily is very small.
Is compound interest good or bad?
It is great when you are earning it (savings, investments). It is costly when you are paying it (credit cards, loans). The same math that grows your savings also grows your debt.
How much does $10,000 grow in 20 years?
At 7% compounded annually, $10,000 becomes $38,697 in 20 years. At 5%, it becomes $26,533. The rate makes a big difference over long periods.
What is the Rule of 72?
Divide 72 by your interest rate to estimate how many years it takes for your money to double. At 6%, money doubles in about 12 years (72 ÷ 6 = 12).
Does inflation affect compound interest?
Yes. If you earn 5% interest but inflation is 3%, your real growth is only about 2%. Always consider inflation when planning long-term savings.
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