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# ADMS3530-Midterm-F10-Sol - 3530 Midterm Exam F2010...

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3530 Midterm Exam – F2010 –Solutions 1. You are planning to establish a 20-year scholarship fund at York University that will pay \$25,000 at the end of the first year and then increase by 1.5% per year. The manager expects that the fund will earn a 5.75% annual rate of return. How much should you donate to York today in order to maintain this scholarship? A) \$50,346 B) \$146,508 C) \$278,225 D) \$329,235 E) \$588,235 Solution : D This is a growing annuity. PV = 588,235.29 x (1 – 0.4403) = 329,235.29 (answers may vary slightly due to rounding) 2. Compute the present value of the following set of payments for two years: \$300 each quarter for the first year and \$600 each quarter for the second year. The effective annual rate is 6% and payments will begin at the end of the first quarter. A) \$3,000.56 B) \$3,340.77 C) \$3,514.06 D) \$3,854.02 E) \$3,999.14 Solution B The quarterly interest rate is (1+ .06) 1/4 -1 = . 01467 =1.467% Using your calculator: PV Annuity 1: PMT= 300; n=4, FV = 0; I/Y = 1.467, COMP PV b PV1 = \$1,157.25 PV Annuity 2 : PMT= 600; n=4, FV = 0; I/Y = 1.467, COMP PV at start of year 2 b PV = 2314.50 and bring back to time zero: PV2 = 2314.50 / (1.01467) 4 = 2,183.52 PV entire stream: = 1157.25 + 2183.52 = \$ 3,340.77 + + - - = T r g g r C annuity growing of PV 1 1 1 1 + + - - = 20 1 0575 . 1 015 . 1 1 015 . 0575 . 000 , 25 annuity growing of PV

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3. How much will be in an account after 15 years if the initial deposit was \$2500 and it earned interest at an APR of 6%, compounded monthly? A) \$1,018.71 B) \$1,242.42 C) \$2,735.88 D) \$5,030.49 E) \$6,135.23 Solution E im = APR/m = 6%/12 = .0050 or .50% FV= 2500 x (1.005)^180 = \$6,135.23 4. What is the effective annual rate on a deposit of \$3,000 made eight years ago if the deposit is worth \$4,453.52 today? The deposit pays interest semi-annually. A) 2.50% B) 5.00% C) 5.06% D) 10.12% E) 12.50% Solution C Using your calculator: PV= -3,000 FV= 4,453.52 N=16 PMT =0 COMP I/Y b I/Y = 2.50% this is the semi-annual rate EAR = (1+ .025)^2 -1 = 5.06% 5. You are planning to buy a new condominium in Toronto. The Condo is worth \$400,000; you will put a 10% down payment and obtain a 25-year fixed rate mortgage at 6.25% (APR semi-annually compounded) for the rest. You have decided to make weekly payments which will begin at the end of the first week. What is your weekly payment? (Assume there are 52 weeks in one year.) A) \$542.81 B) \$608.42 C) \$735.66 D) \$808.21 E) \$923.55 Solution: A 1 . Find Semi-annual rate: i s = 6.25% -> .0625/2 = .03125 2. Find EAR: EAR = (1.03125) 2 – 1 = .06348 3. Find the weekly rate: i w = (1+ 0.06348) 1/52 -1 = 0.001184
4. Find Number of payments in mortgage: n = 25yrs x 52wks/yr = 1300 weeks 5. Find the monthly payment with a PV of \$360,000 (\$400,000 x 90% ) Using your calculator: PV= - 360,000, n=1300, i =0.1184%, FV=0, PMT=? Answer= \$542.81 6. You believe that you will need \$1,500,000 when you retire in 35 years from today. You also know that you will receive an extra payment of \$100,000 from your trust fund in

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ADMS3530-Midterm-F10-Sol - 3530 Midterm Exam F2010...

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