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ORIE 350 Lecture 9

ORIE 350 Lecture 9 - 1 = Payment at first annuity period =...

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ORIE 350 Lecture 9 Today: Time value of money Bonds Wednesday: Leases Thursday: prelim 1 HO 110 and B-14 Time value money Interest expense on a construction loan is added to the cost of the asset itself 10,000,000 Building 9,000,000 Loan at 6% (9,000,000) x 0.06= 540,000 Building(A) 10,540,000 Time value of money FV= PV(1+i) n Be careful that i and n match, e.g. i is the monthly rate and n is the number of months (used for monthly compounding) To get i: i = i nom / C i nom = nominal annual rate i = periodic rate C = no. Of compounding periods per year Annuity
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Multiple periodic payment of a fixed and constant amount. Business applications 1. Some loans 2. All bonds (except zero coupon bonds) 3. All leases Personal applications 1. Car loans 2. Home mortages On a time line Give me 8,000 now and I will give u 2,000 dollars every year for 5 years Ordinary annuity-> payment occurs at the end of each period Annuity Due-> payment at the beginning of each period e.g lease for apartments PV
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Unformatted text preview: 1 = Payment at first annuity period = A/(1+i) PV 2 = A 2 /(1+i) 2 Total present value = PV 1 + PV 2 + PV 3 + . ..+ PV n To make it into a geometric series, add A in front and subtract A from the present value after that PV= A(1-(1+i)-n )/ i) FV= A((1+i) n-1)/i) In class examples 1 a. FV= 120,000 i=9% n= 8 years(matches interest rates) PV=? Single payment today PV= FV/(1+i) 8 = 120,000/(1.09) 8 =60,223.95 b. PV= 120,000(1.05) 8 / (1.09) 8 = 83,973.21 2. PV = 10,000 I nom = 3% C =12 n=42 months FV=? 1. Convert i = i nom /C I= 0.03/12= 0.0025 2. FV= PV(1+) n = 10,000 (1.0025) 42 = 11,105.65 3. Ordinary annuity PV= ? A= $2,250 per year I= 10% per year N= 15 years Note compounding frequency = payment frequency for annuities PV= 2250 x (1-(1.1)-15 )/0.10)= 17,113.68 4. Deposits are monthly, means compounded monthly FV= A[(1+i) n-1/i] x (1+i) = 200[(1+0.07/12) 180-1/(0.07/12)] x (1+0.07)= 63,762.25...
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