Time Value of Money (CFA Level 1 Quant)

Time value of money (TVM) underlies bond pricing, equity valuation, and capital budgeting. Getting fluent here pays off across the entire CFA curriculum, not just the Quantitative Methods topic.

Key Takeaways

  • Every TVM problem links five variables — PV, FV, N, I/Y, PMT — solve for any one given the other four.
  • An annuity due is worth more than an ordinary annuity because each payment is discounted one fewer period.
  • Convert the stated annual rate to a periodic rate and adjust N to match the compounding frequency.
  • Sign errors (not concept errors) cause most TVM mistakes — keep cash outflows negative and inflows positive.

The core idea

A dollar today is worth more than a dollar tomorrow because it can earn a return. Every TVM problem connects five variables:

  • PV — present value
  • FV — future value
  • N — number of periods
  • I/Y — interest rate per period
  • PMT — periodic payment (for annuities)

Given any four, you solve for the fifth.

Present and future value

  • FV = PV × (1 + r)^N
  • PV = FV / (1 + r)^N

If you invest $1,000 at 6% for 3 years: FV = 1,000 × 1.06^3 ≈ $1,191.

Annuities

An ordinary annuity pays at the end of each period; an annuity due pays at the beginning. An annuity due is worth more because each cash flow is discounted one period less. On most calculators you switch between them with a BGN/END setting — a frequent source of wrong answers when left in the wrong mode.

Compounding frequency matters

The periodic rate is the stated annual rate divided by the number of periods per year, and N is years × periods per year. For 8% compounded quarterly over 2 years: I/Y = 2% and N = 8. More frequent compounding raises the effective annual rate.

Calculator discipline

Clear the worksheet between problems and enter cash outflows as negative and inflows as positive — sign errors, not concept errors, cause most TVM mistakes under time pressure. Exact keystrokes differ between the two CFA-approved calculators (TI BA II Plus and HP 12C), so practice on your specific model well before exam day rather than relearning it under time pressure.

Drill TVM and the rest of Quant with our diagnostic practice questions, and build a schedule with our 6-month CFA study plan.

Educational overview only. Confirm formulas and calculator policy against current CFA Institute materials. Not affiliated with CFA Institute.

Time Value of Money: CFA L1 Quant | Sophos Academy