By Harry Prabandham · Updated September 28, 2026
Personal Finance
Compound Interest and the Time Value of Money, Explained
Compound interest earns returns on prior returns, so time matters. The Rule of 72 estimates doubling time; inflation, taxes, and fees reduce real growth.
Compound Interest and the Time Value of Money, Explained
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What is compound interest?
- Compound interest is interest earned on both the original amount and on interest already credited.
- Simple interest pays only on the original principal, so the balance grows in a straight line.
- Because each period's growth builds on the last, the effect of compounding increases with time.
- Investment returns aren't fixed like interest; they can be negative, and losses compound too.
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What is compound interest?
- Compound interest is interest earned on both the original amount and on interest already credited.
- Simple interest pays only on the original principal, so the balance grows in a straight line.
- Because each period's growth builds on the last, the effect of compounding increases with time.
- Investment returns aren't fixed like interest; they can be negative, and losses compound too.
What is the Rule of 72?
- Divide 72 by an annual growth rate to estimate how many years something takes to double at that rate.
- It's a mental shortcut that is reasonably accurate for rates in the mid-single digits to low teens.
- It works for costs too: prices rising 3% a year double in about 24 years.
- For investments, the rate is an assumption rather than a known figure, so any doubling time is only an estimate.
Why does starting earlier matter?
- Money invested earlier has more years for growth to build on itself.
- Money added later has fewer years to compound, so reaching the same goal typically takes larger contributions.
- Early contributions can become a large share of a long-term balance, depending on the returns actually earned.
- A long horizon doesn't remove market risk, and declines along the way affect the outcome.
How do compounding frequency and debt fit in?
- Interest can compound daily, monthly, quarterly, or annually, and more frequent compounding raises the effective yield slightly.
- Federal Truth in Savings rules require banks to quote annual percentage yield (APY), which reflects compounding and makes rates comparable.
- Reinvesting dividends and interest lets that income compound instead of sitting as cash.
- Compounding works against borrowers when unpaid interest is added to a balance that then accrues more interest.
How do inflation, taxes, and fees reduce compounding?
- Real return is roughly the nominal return minus inflation, and it's what determines purchasing power.
- Taxes paid each year on interest, dividends, and realized gains leave less money to compound.
- Traditional 401(k)s and IRAs defer tax until withdrawal, and qualified Roth withdrawals are tax-free.
- Fund expenses and advisory fees are subtracted every year, so they compound against you as well.
What are present value and future value?
- Future value estimates what an amount today grows to at a given rate over a given time.
- Present value works backward, converting a future amount into today's dollars using a discount rate.
- These tools underpin loan pricing, pension lump-sum offers, retirement projections, and business valuation.
- The results are only as reliable as the rate assumption behind them.
Key takeaways
- Compounding rewards time, whether it's working for you as a saver or against you as a borrower.
- The Rule of 72 is a quick estimate of doubling time at a given rate.
- Inflation, taxes, and fees all reduce the real growth that compounding delivers.
- Any projection depends on assumed rates, and investment returns aren't assured.
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