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ADM2350 (26)
Lecture 5

ADM2350 Lecture 5: Untitled5
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Department
Administration
Course
ADM2350
Professor
Anna Dodonova
Semester
Fall

Description
Canadian Mortgage Loans: A two-step procedure is applied to calculate the monthly rate in order to calculate the monthly payment: a. First, convert the APR to EAR: EAR = (1 + 6%/2)^2 – 1 = 6.09% b. Second, calculate the monthly rate (r) with the same EAR as 6.09%: 6.09% = (1 + r)^12 – 1 c. Solve the above equation, r = 0.00494 Growing Annuities and Growing Perpetuities: —> Growing annuity is a series of finite cash flows that grow at a fixed rate. —> Growing perpetuity is a constant stream of cash flows without end that is expected to rise indefinitely. —> Note: “grow” does not necessary means “increase”: the growth rate can be positive or negative e.g, Assume your starting salary after graduation is $40,000 and it expects N to grow at 10% annually until you retire. What is the PV of all your fCtur⎪ ⎡1+g ⎤ ⎪ expected salary if you will be in employed for 40 years ant the interest rate ⎢ ⎥ ⎬ I −g ⎩ ⎣1+I ⎦ ⎭ is 6% I=0.06 = interest rate g=0.1 = growC=$40,000 = cash payment at the first period Thus, PV = $3,400,203 e.g, What is the value of a growing perpetuity with the first payment of $1,000 and the PV = growth rate of 4% if the interest rate is 12%? I −g I=0.12 = interest rate g=0.04 = growth rate C=$1,000 = cash payment at the first period —> NOTE: we must have r>g in order to have the finite value of a perpetuity Thus, PV = $1,000/(0.12-0.04)=$12,500 e.g, you will live for 20 years after you retire and you want to be able to spend $40,000/year. You plan to retire in 40 years and want to contribute an equal amount of money into your saving plan each year starting next year. What your annual contributions should be if the interest rate is 5% a. First, find PV of your future withdrawals. N=20; I=5%, PMT = 40,000, FV = 0 Thus, PV (at N=40) = $498,488 b. Therefore, PV (at N=0) = $ 498,488 /(1.05^40)= $70,808 The PV of your savings must be equal to the PV of your withdrawals: PV = - $70,808; N=40; I=5%. Thus, PMT = $4,127/year. e.g, You think, you will live for 20 years after you retire and you want to be able to spend $40,000/year adjusted for inflation. Assuming the inflation rate is 2%/year it means that you need $40,000*(1.02^41)=$90,088 in your first retirement year and this figure grows with the rate of 2%/year. You plan to retire in 40 years and want to contribute an equal percentage of your salary into your saving plan each year starting next year. Your salary next year will be $40,000 and you expect it to grow 8% per year. What
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