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Personal Finance
Compound Interest and the Time Value of Money
How compound interest works, why starting early matters, the Rule of 72, and how inflation and taxes affect the real growth of your savings and investments.
Compound Interest and the Time Value of Money
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What Compound Interest Is
- Compound interest earns returns on both the original principal and accumulated interest
- Simple interest pays only on the original principal, growth is linear, not exponential
- The longer money compounds, the faster the balance accelerates
- Most savings accounts, bonds, and investments use some form of compounding
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What Compound Interest Is
- Compound interest earns returns on both the original principal and accumulated interest
- Simple interest pays only on the original principal, growth is linear, not exponential
- The longer money compounds, the faster the balance accelerates
- Most savings accounts, bonds, and investments use some form of compounding
The Rule of 72
- Divide 72 by the annual return rate to estimate years to double your money
- At 6% annual return, money doubles in roughly 12 years; at 8%, roughly 9 years
- The rule is a quick mental shortcut that works best for rates between 4% and 12%
- $10,000 at 7% compound interest grows to about $19,672 after 10 years
The Power of Starting Early
- Investing $500 per month from age 25 to 65 at 7% yields roughly $1.2 million
- Waiting until age 35 to start the same plan yields roughly $567,000, less than half
- The first 10 years of contributions can represent a large share of the final balance
- Time in the market, not timing the market, is the primary driver of wealth accumulation
Compounding Frequency and Real-World Applications
- Interest can compound daily, monthly, quarterly, or annually with modest differences
- Reinvested dividends and capital gains compound investment portfolio growth
- Compounding works against you too, credit card debt grows the same way
- Loan amortization schedules show how interest compounds on outstanding balances
How Inflation Erodes Compounding
- Inflation reduces the purchasing power of future dollars earned through compounding
- A 7% nominal return with 3% inflation produces roughly 4% real growth
- Over 30 years, 3% inflation cuts a dollar's purchasing power by more than half
- Always consider real, inflation-adjusted returns when projecting long-term growth
Tax Drag on Compounding
- Taxes on interest, dividends, and gains reduce the amount available to compound
- A taxable account earning 7% might effectively compound at 5% or less after taxes
- Tax-deferred accounts like 401(k)s and IRAs let the full return compound until withdrawal
- Tax-free accounts like Roth IRAs eliminate tax drag entirely on qualifying gains
Present Value vs. Future Value
- Future value calculates what today's money will be worth at a given growth rate
- Present value calculates what a future sum is worth in today's dollars
- These concepts underpin retirement planning, loan pricing, and investment analysis
- Start saving early and minimize fees and taxes to maximize the compounding cycle
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