L02 Time Value of Money - Lehigh University

Time Value of Money

Mathematics of Finance Compounding and Discounting

Copyright ?2003 Stephen G. Buell

Reasons for interest

Lender's side

? Reward for postponing consumption ? Compensation for risk

? Default risk ? Purchasing power risk (inflation) ? Liquidity risk

Borrower's side

? Productivity of capital ? Reinvest the funds at a higher rate

Copyright ?2003 Stephen G. Buell

Mathematics of finance

P0 = principal at time 0 St = future sum at time t n = number of compounding years i = interest rate per year

Copyright ?2003 Stephen G. Buell

1

Lump-sum compounding

S1 = Po + P0i S2 = S1 + S1i S2 = P0 ( 1 + i )2 Sn = P0 ( 1 + i )n (1 + i )n = ( FVIF ? i% - n )

( FVIF ? i% - n ) = Future Value Interest Factor for i% and n years

Copyright ?2003 Stephen G. Buell

Simple example

If P 0 = $25, n = 5 and i = 6% S5 = 25(1.06)5 = 33.46 S5 = 25(FVIF ? 6% - 5) S5 = 25(1.3382) = 33.46

Using a financial calculator: 25?PV 6?I/yr 5?n FV=33.46

$25 invested today at 6% will grow to $33.46 in 5 years

Copyright ?2003 Stephen G. Buell

Frequency of compounding

Bonds

Semiannually 2 times/yr

Savings Accts

Quarterly

Car Loans & Monthly Mortgages

MC/Visa Daily

4 times/yr 12 times/yr 365 times/yr

Copyright ?2003 Stephen G. Buell

2

Quarterly compounding

Sn = P0 ( 1 + i )n i = interest rate per period n = number of periods Passbook offers 8%/yr comp quarterly i = 2%/period and n = 4 periods/yr S1Q = P0(1.02) S2Q = P0(1.02)(1.02) S4Q/1yr = P0( 1.02)4

Copyright ?2003 Stephen G. Buell

Effective Annual Rate

EAR = $Interest = S1yr - P0

Principal

P0

EAR = P0(1.02)4 - P0 = (1.02)4 - 1= 8.24%/yr P0

EAR = (1 + i)n -1 ................
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