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AK/ADMS 3530.03 Finance Midterm Exam Winter 2007 Solutions Type A Exam Numerical questions (4 points each) 1. (Q. 2 in B) The Joshua Co. plans on saving money to buy some new equipment. The company is opening an account today with a deposit of \$15,000 and expects To earn 4% interest annually. After 3 years, the firm wants to add an additional \$50,000 to the account. If the account continues and earns 4% interest compounded semi-annually after 3 years, how much money will the Joshua Co. have in their account five years from now? A) \$66,872.96 B) \$68,249.79 C) \$70,952.96 D) \$72,385.44 Answer D Using FV = PV × (1+r)^t formula FV in 3yrs = \$15,000 × (1 + 0.04) ^3 = \$16,872.96 FV in 5 yrs = \$(16,872.96 + 50,000) × (1 + 0.04 / 2)^ 4 = \$72,385.44. 2. (Q. 1 in B) I want to buy a car that I know will cost me \$43,860 (before taxes) in ten years. How much must I save annually, beginning one year from now, in order to accumulate the purchase price plus all applicable taxes by the end of Year 10? In this case taxes are 6% GST and 8% PST which are each applied to the purchase price. Assume that interest is calculated at 9 percent annually. Answer B 1

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Amount required in ten years = \$43,860 × (1.14) = \$50,000.40 Using the FV annuity formula where FV= PMT× ((1+r)^t – 1) r \$50,000 = PMT × ((1.09) 1) .09 10 - = PMT × 15.1929 PMT = \$3,291.04. 3. (Q. 8 in B) A credit card company sends you a promotion that says it will charge you an interest rate of 1.25% monthly. In this case the annual percentage rate (APR) is ____ and the effective annual rate (EAR) is _______ and if I carried a \$300 balance throughout the year I would owe _______ at the end of the year. Answer D APR = 1.25% × 12 = 15% EAR = (1+1.25%)^12 – 1 = 16.08% Balance owing = 300 × (1+0.1608) = \$348.24. 4. (Q. 9 in B) Prizes are often not “worth” as much as claimed. Place a value on a prize of \$5,000,000 that is to be received in equal annual payments over the next 20 years, with the first payment beginning today. Assume an interest rate of 7 percent over the 20-year period. Answer C 2
Annual payment = \$5,000,000 / 20 = \$250,000 PV = PMT + PMT 1 i 1 (1 i) i n - + (for annuities due) = \$250,000 + \$250,000 1 .07 1 07(1.07) . 19 - = \$250,000 + \$250,000 [10.3356] =\$2,833,898.81. 5. (Q. 3 in B) Which of the following strategies will allow real retirement spending to remain approximately equal, assuming savings of \$1,000,000 invested at 8 percent annually, a 25-year time horizon, and a 4 percent expected annual inflation rate? A) Spend approximately \$63,000 annually. B) Spend approximately \$78,225 annually. C) Spend approximately \$93,680 annually. D) Spend approximately \$127,500 annually. Answer A Using the formula where 1 + real rate = rate inflation 1 rate nominal + + 1 Real rate = 1.08 1.04. – 1 = 3.85%. Then using the formula where PV of an annuity = + - × t ) r 1 ( r 1 r 1 C \$1,000,000 = pmt 1 .0385 1 .0385(1.0385) 25 - \$63,001 = pmt . 6. (Q. 4 in B) You are saving money to buy a house in ten years. You will need \$75,000 to make the down payment at that time. Due to some other financial commitments you won’t be able to deposit any money in years 9 and 10 towards this down payment. How much equal amounts must you deposit in a savings account at the end of each year (other than years 9 and 10) in order to save \$75,000 if the savings account pays interest at 10 percent per year compounded annually?

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