Single Payments & Discrete Compounding

Timing of Cash Flows

• Discrete models: cash flows & compounding occur at the end of fixed periods (years, months)
• Continuous models: assume cash flows/compounding are continuous (approximation

Common Cash Flow Patterns

• Single payment: one time inflow/outflow
• Annuity: equal payments each period
• Arithmetic gradient: payments increase/decrease by a fixed amount
• Geometric gradient: payments grow/decay by a fixed %

Single Disbursements/Receipts

• Future worth of a present value: what is F given P, i, and N?

  $$ F = P(1+i)^N \text{ or } (\frac{F}{P}, i, N) = (1+i)^N $$

• Present worth of a future value: what is P given F, i, N?

  $$ P = \frac{F}{(1+i)^N} \text{ or } (\frac{P}{F}, i, N) = \frac{1}{(1+i)^N} $$

Annuities (Uniform Series)

Equal payments $A$ at the end of each period for $N$ periods

Sinking Fund Factor

• Uniform payment $A$ to accumulate future value $F$

$$ (A/F, i, N) = \frac{i}{(1+i)^N-1} $$

Uniform Series Compound Amount Factor

• Equal payment $A$ equivalent to future value $F$