THE TIME VALUE OF MONEY. Time Value of Money  Is a dollar today worth more than a dollar tomorrow?  YES  Why?  Opportunity cost & inflation  This.

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Presentation transcript:

THE TIME VALUE OF MONEY

Time Value of Money  Is a dollar today worth more than a dollar tomorrow?  YES  Why?  Opportunity cost & inflation  This is the reason for charging and paying interest

Time Value of Money  Let v = future value of $ p = present value of $ r = real interest rate (nominal rate – inflation rate) expressed as a decimal n = years k = number of times interest is credited per year  The Simple Interest Formula v = ( 1 + r ) n * p  The Compound Interest Formula v = ( 1 + r / k ) nk * p

Time Value of Money - Illustrated  Assume that inflation is expected to be 3% and that the nominal interest rate on simple interest savings is 1%. Calculate the future value of $1 after 1 year.  Step 1: Calculate the real interest rate r% = i% -  % r% = 1% - 3% = -2% or -.02  Step 2: Use the simple interest formula to calculate the future value of $1 v = ( 1 + r ) n * p v = ( 1 + (-.02)) 1 * $ 1 v = (.98) * $ 1 v = $0.98

Time Value of Money - Illustrated  Assume that inflation is still expected to be 3% but that the nominal interest rate on simple interest savings is 4%. Calculate the future value of $1 after 1 year.  Step 1: Calculate the real interest rate r% = i% -  % r% = 4% - 3% = 1% or.01  Step 2: Use the simple interest formula to calculate the future value of $1 v = ( 1 + r ) n * p v = ( ) 1 * $ 1 v = $1.01

Time Value of Money - FUN!!!  Assume that annual inflation is expected to be 2.5% and that the annual nominal interest rate on a 10 year certificate of deposit is 5% compounded monthly. Calculate the future value of $1,000 after 10 years.  Step 1: Calculate the real interest rate r% = i% -  % r% = 5% - 2.5% = 2.5% or.025  Step 2: Use the compound interest formula to calculate the future value of $1,000 v = ( 1 + r / k ) nk * p v = ( / 12 ) 10*12 * $1,000 v = ( ) 120 * $1,000 v = $1,283.69

Relating Money to GDP  Economist, Irving Fisher postulated that :  Nominal GDP = The Money Supply * Money’s Velocity

The Monetary Equation of Exchange  MV = PQ  M = money supply (M1 or M2)  V = money’s velocity (M1 or M2)  P = price level (PL on the AS/AD diagram)  Q = real GDP ( sometimes labeled Y on the AS/AD diagram)  P * Q or PQ = Nominal GDP

The Monetary Equation of Exchange  MV=PQ  M1=$2 trillion  V of M1 = 7  PQ = $14 trillion GDP R PL AD SRASLRAS QFQF P