Compound Interest & Time Value of Money
Money you have today is worth more than the same amount tomorrow — because it can earn interest. Compounding is how that earning snowballs.
What compounding actually is
When you earn interest, that interest itself starts earning interest the next period. That's compounding. The longer the runway, the more it dominates the original amount you put in.
Plain English: interest on interest. It's the reason a single retirement contribution at 22 can be worth more at 65 than a much larger one at 45.
Why "time value of money"
$100 today > $100 a year from now. Because today's $100 could earn a year of return, the future $100 is worth less today. We "discount" future dollars to compare them fairly to present ones.
Two directions: Future Value (FV) projects today's money forward. Present Value (PV) pulls future money back to today.
The compound interest formula
A = P × (1 + r/n)n·tA final amount · P principal · r annual rate (decimal) · n compounds per year · t years. As n → ∞ (continuous compounding), A = P·er·t.
Interactive calculator
Year-by-year breakdown
| Year | Start | + Contrib | + Interest | End |
|---|
Simple vs Compound
Simple interest $0
Interest only on the original principal. Same every period.
A = P · (1 + r · t)Compound interest $0
Interest earns interest. Curves up — small at first, dramatic at the end.
A = P · (1 + r/n)n·tThe Rule of 72
Years to double ≈ 72 ÷ rate%. A back-of-napkin shortcut for compounding. At 6%, money doubles in 12 years; at 9%, in 8.
Present & Future Value
Future Value of $1,000 today
At the calculator's rate & years above. FV = PV·(1+r)t
Present Value of $1,000 future
What $1,000 in the future is worth today. PV = FV / (1+r)t
Inflation chew
Buying power of $1,000 after 30 years at 3% inflation.
Connect the dots
Quiz
15 questions on compounding mechanics.
Flashcards
Tap to flip. Twenty essential terms.
Teacher mode
Formulas, lesson outline, and a printable worksheet with answer key.
Lesson outline (40 min)
- 5 min · Hook — Show the Rule of 72 grid. Ask: "Which doubles your money faster — saving $100/mo at 8%, or starting with $1,000 at 0%?"
- 10 min · Concept — Derive A = P(1+r/n)nt from "interest on interest." Walk one $1,000 @ 10% example by hand for two years.
- 10 min · Calculator demo — Show how doubling time changes with rate. Compare 6% to 12% over 30 years (it's not 2×; it's much more).
- 10 min · Worksheet — Students work the printed problems. Most are pencil-and-paper friendly; calculator allowed.
- 5 min · Wrap — Discuss: why the same dollar contribution at 22 beats double at 35. Time is the lever, not the amount.