Time Value of Money

6.1 Time is money

• “Interest”
• “Interest rate”

6.2 Real and Nominal Interest Rates

nominal interest rate:

• the interest rate usually reported and not corrected for inflation.

real interest rates:

• The real interest rate at which the purchasing power of money remains constant.
  Real interest rate = Nominal interest rate – Inflation rate
• effective interest rate. In compound interest method calculation, the effective interest rate generated because the interest period is shorter than one year.

  i = (1+ r/m) ^m – 1
  i = real annual interest rate
  r = nominal annual interest rate
  m = number of compounding periods in a year

6.3 Interest Calculation

Naming Conventions in Interest Formulas:

• P - "Principal Amount": how much is the money worth right now? Also known as “present value” or “present worth”.
• F - "Final Amount": how much will the money be worth at a later time? Also known as “future value” or “future worth”.
• i - "Interest rate per period". Assumed to be annual unless stated otherwise.
• n - Number of interest periods between points in time.
• A - "Annuity": a stream of equal, recurring payments due at the end of each interest period.

I = P × n × i
F = P + I = P (1 + ni)
Single-Payment Compound-Amount (F/P):
F = P ( 1 + i )ⁿ

6.4 Equivalence

Two or more different cash-flow instances (cash-flow streams) are equivalent at a given interest rate, only when they equal the same amount of money at a common point in time.