2
Quantitative MethodsModule 2 of 11

Time Value of Money in Finance

7

Concepts

7

Formulas

2

Decisions

6

Quiz Questions

Key Concepts

7 concepts covered in this module.

Present Value (PV)

The current worth of a future cash flow discounted at the appropriate rate. Foundation of all valuation.

Future Value (FV)

The value of a current amount after earning interest over a specified period.

Annuity

A series of equal cash flows at regular intervals. Ordinary annuity: payments at END. Annuity due: payments at BEGINNING.

Perpetuity

An annuity that pays forever. PV = PMT/r. Growing perpetuity: PV = PMT/(r - g).

Cash Flow Additivity

PV of a series of cash flows equals the sum of the PVs of individual cash flows. Basis for no-arbitrage pricing.

Implied Return

The discount rate that equates the PV of future cash flows to the current market price. For bonds: YTM; for stocks: implied return from DDM.

Implied Forward Rate

Future interest rate implied by current spot rates via no-arbitrage. (1+S2)² = (1+S1)(1+f1,1).

Formulas

7 essential formulas for this module.

Future Value

FV = PV × (1 + r)n

Where: r = interest rate per period, n = number of periods

Present Value

PV = FV / (1 + r)n

Where: r = discount rate, n = periods

PV of Ordinary Annuity

PV = PMT × [(1 - (1+r)-n) / r]

Where: PMT = periodic payment

PV of Perpetuity

PV = PMT / r

Where: PMT = periodic payment, r = discount rate

PV of Growing Perpetuity

PV = PMT / (r - g)

Where: g = growth rate (must be < r)

EAR (Effective Annual Rate)

EAR = (1 + rperiodic)m - 1

Where: m = compounding periods per year

Implied Forward Rate

(1 + Sn)n = (1 + Sn-1)n-1 × (1 + fn-1,1)

Where: S = spot rate, f = forward rate

Decision Frameworks

2 decision frameworks to guide your analysis.

Ordinary Annuity vs Annuity Due?

  • Ordinary annuity: most bonds (coupons at end of period), most loans
  • Annuity due: lease payments at start, insurance premiums

When to use Cash Flow Additivity?

  • Pricing bonds by discounting each coupon separately at spot rates
  • No-arbitrage pricing of derivatives
  • Implied forward rate calculations

Mind Map

Visual overview of how concepts connect in this module.

Time Value of Money
Single Cash Flow
FV = PV(1+r)^n
PV = FV/(1+r)^n
Compounding vs Discounting
Annuities
Ordinary (end of period)
Annuity Due (beginning)
PV and FV formulas
Adjust: ×(1+r) for Due
Perpetuities
PV = PMT/r
Growing: PMT/(r-g)
Gordon Growth Model link
Cash Flow Additivity
Sum of individual PVs
No-arbitrage pricing
Forward rate derivation
EAR & Compounding
EAR = (1+r/m)^m - 1
Continuous: EAR = e^r - 1
Always > stated rate

Study Time Value of Money in Finance

This module has 16 flashcards and 6 quiz questions to test your knowledge.

Open the study dashboard to access interactive flashcards, timed quizzes, and track your progress.

Open Study Dashboard

No signup required. Create an account anytime to save progress.

Previous Module

Rates and Returns

Next Module

Statistical Measures of Asset Returns