Library
Foundations of Financial Planning · 12 of 12
Foundations of Financial Planning
finance CRITICAL

Time Value of Money and Compound Interest

Foundations of Financial Planning
compound-interest future-value present-value annuity time

Key Principle

A dollar today is worth more than a dollar tomorrow because today's dollar can earn interest. This principle operates in two directions: compounding (forward -- what will I have?) and present value (backward -- what must I do today?). Without both directions, financial planning is incomplete. Compounding answers projection questions; present value reverse-engineers the actions required to reach a target.

Why This Matters

Time is the dominant variable in wealth accumulation, not contribution size. Compounding creates exponential growth where interest earns interest, and the effect accelerates dramatically with longer time horizons. This is why starting early matters more than contributing more: a person who starts 10 years earlier can contribute less per year and still end up with more. Every year of delay costs disproportionately because the lost compounding cannot be recovered by simply increasing contributions later.

Good Examples

  • Compounding demonstration: $2,000/year for 20 years at 5% yields $66,132 -- not the $40,000 deposited. The $26,132 difference (65% bonus) is pure compounding (p. 64).
  • 401(k) power: An extra $100/month to a 401(k) at 6% for 25 years produces approximately $70,000 -- a 2.3x return on total contributions (p. 61).
  • Naive math overestimates required savings: Dividing a $45,000 goal by 6 years yields $7,500/year. The actual required savings at 5% return is $6,616/year -- an $884/year overestimate. Over 6 years, TVM-ignorant planning forces you to save ~$5,300 more than necessary (p. 64).
  • Two-step goal method: $5,000 existing savings grows to $6,700 at 5% over 6 years. The remaining $38,300 gap requires only $5,630.70/year instead of $6,616 from scratch (pp. 64-65). This approach is both more accurate and less discouraging than calculating from zero.
  • Retirement withdrawal transformation: Dividing $300,000 by 30 years yields $10,000/year. But because remaining funds keep earning interest, TVM-adjusted sustainable withdrawal is $19,514.73/year -- nearly double (p. 66). This is the single most consequential finding in the chapter for retirement planning.
  • Annuity pricing: A payment stream of $700/year for 5 years at 5% discount rate has a present value (maximum purchase price) of $3,030 (p. 67). This same framework applies to evaluating any stream of future cash flows.

Counterpoints

  • TVM calculations assume a constant rate of return, which real investments do not provide. Sequence-of-returns risk (bad years early in retirement) can devastate withdrawal plans even when the average return matches assumptions.
  • The two-step goal method is more accurate and less discouraging than calculating from zero, but both still depend on actually achieving the assumed rate of return.
  • The annuity formula is bidirectional: the same formula that calculates required savings also calculates sustainable withdrawals and prices annuity purchases. One tool serves both accumulation and distribution phases (pp. 66-67).
  • TVM-ignorant planning creates errors in both directions: it overstates required savings (discouraging people from starting) and understates sustainable retirement withdrawals (causing unnecessary frugality in retirement). Both errors are psychologically harmful.

Key Quotes

  • "In the final analysis, a cash budget has value only if (1) you use it and (2) you keep careful records of actual income and expenses." (p. 62) -- connecting TVM goals back to the budget system that funds them
  • Present value is "the inverse of compounding." (p. 66)
  • The chapter positions TVM as the bridge between goal-setting and action: financial statements reveal current position, ratio analysis diagnoses health, the cash budget controls spending, and time value of money "translates goals into precise dollar targets" (pp. 67-68). Removing any component breaks the feedback loop.

Rules of Thumb

  1. Rule of 72: Divide 72 by the interest rate to estimate how many years it takes money to double. At 6%, money doubles in ~12 years; at 8%, in ~9 years.
  2. Two-step goal quantification: (1) Calculate the future value of existing savings (lump sum FV), then (2) calculate required annual savings to close the remaining gap (annuity calculation). This is always more accurate than ignoring existing assets (pp. 64-65).
  3. PV formula: Present Value = Future Value x Present Value Factor (factor looked up by discount rate and time period, Appendix C). For annuities, use annuity factors from Appendix D (p. 66).
  4. Naive division always gets it wrong: Dividing a goal by years ignores both the growth of existing savings and the compounding of future contributions. The error runs in both directions -- oversaving toward goals, and underestimating sustainable retirement withdrawals.
  5. Time beats amount: Starting earlier with smaller contributions outperforms starting later with larger ones, because compounding rewards duration more than size.

Related References