Introduction to Finance- Week 2 (Chapter 5&6)
Introduction to Finance- Week 2 (Chapter 5&6) Fin 301
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This 3 page Class Notes was uploaded by Rodriguez Notetaker on Monday January 11, 2016. The Class Notes belongs to Fin 301 at Drexel University taught by Dr. Tricia Robak in Fall 2016. Since its upload, it has received 16 views. For similar materials see Principles of Finance in Finance at Drexel University.
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Date Created: 01/11/16
Week 2 notes (Chapter 5 & beginning of 6 ) Time Value of Money “a dollar saved is a quarter earned” Is all about interest The value of money today may not be the same tomorrow or any point of time in the future o We have to accept this Define the variables o P 0 Present Value (PV)/ Principal at time= 0 o P=tFuture Value (FV)/ Future sum at time=t t is some point in time o n= number of compounding periods compound interest: interest of on interest* o i= interest rate invest $P for a year at i. o How much will we have at the end of one year? P 1 P 0+ P 0 =P0(1+i) o How much will we have at the end of the year? P 2P +1 1i) P =P (1+i)+ P (1+i)(i) 2 0 2 0 =P0(1+i) Exponential growth In general: o P n P (0+i) or FV= PV(1+i) n Future value of a lump sum Invest $25 for 5 years at i= 6% What is the value of our investment at the end of 5 years? 5 FV= 25 (1+ .06) = 33.46 It is negative the PV when entered in the calculator it thinks that you are taking it out (as an inflow) they are opposites Various kind of interest: 1. Annual Percentage Rate (APR) The norminal or stated interest rate What is given 2. Periodic Interest Rate (APR/m) The rate per period (e.g day week month) m= # of compounding periods per year Used in TVM calculation this is the rate it is talked about 3. Effective Annual Rate (EAR) The true rate when compounding is considered o Example: Passbook Saving account advertises 8%/year compounded quarterly APR type of interest rate o 1= 0.08/4= 0.02/quarter o P0=1.00 o P1Q 1(1.02)= 1.02 o P2Q 1(1.02)(1.02)= (1.02) 2 o P4Q 1(1.02)(1.02)= (1.02) 4 1.0824 EAR= (1+ APR/m) – 1 o (1 + .08/4) – 1= 0.0824= 8.24% Two investing options: a. 21%, compounded semi annually b .20%, compounded daily (each scenario you have to calculate EAR) When is each rate used: APR= written into contracts, quoted by banks and brokers. Not used in calculations or shown on time lines unless compounding is annual Periodic Rate= used in calculations, shown on time lines. EAR= used to compare returns on different investments with different compounding pattern Present Value of a Lump Sum: Someone offers you 33.46 and promises to pay you in 5 years o What is that investment worth today if the interest rate is 6%? 5 PV= 33.46/(1+.06) What if a bank account that offers 6%, compounded semiannually. You want to accrue 33.46 in 5 years. How much should you deposit today? 10 PV= 33.46/(1+.03) o 10 because it is semiannually o 3% instead of 6% because of semiannually Choice of 2 gifts: o Getting 100 in year 1,2,3 and 250 at year 6 o Getting 325 in year 5 and 6 Annuity: Something annual/ annual payment Series of equal $ amounts being paid or received at equal points in time. (regular intervals) Ordinary annuities payments occur at the end of each period. Annuity begins one period prior to the first payment. o All the cash flows occur at the end of the period Present value of an annuity PV= R n(1+i)n R[ (1+i) 1/i(1+i) ] o Interest factor PV you enter the same values except instead of FV you click payment calculator The payments occur at the end of the period Future Value of an annuity n R[ (1+i) 1/i Future value interest factor of an annuity PMT= Payment Present value of a perpetuity Perpetuity is an annuity but instead of having an end period it has no end—infinitely Example on notebook As n goes bigger and bigger it then becomes 0 o Rewrite: PMT/I Never runs out of money because of interest rate that every year applies
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