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ADMS3530 3.0 Winter 2008 Assignment #1 Question 1 – Time Value of Money (10 marks) Consider a loan for \$100,000 given by a city government to encourage a firm to start a recycling project. The loan would be paid back over eight years by a series of quarterly payments. For the first year, only interest would be charged quarterly. For the next seven years, the loan would be amortized by 28 quarterly payments. The government charges the firm interest at a stated annual rate of 6 percent, whereas a private bank would charge the firm interest at a stated annual rate of 9 percent. Calculate the subsidy conferred by this loan, measured in dollars at the time the loan is disbursed. Answer: First, calculate the interest and annuity payments based on the subsidized annual interest rate of 6%, or quarterly interest rate of 1.5%, for a \$100,000 loan. Quarterly interest payments over the first year = 1.5%*100000 = 1500.00 Quarterly annuity payments for next seven years = 100000/PVAF(1.5%,28) = 4400.11 Second, discount the quarterly annuity payments at the market interest rate of 9%. "PV" of annuity payments after first year = PVAF(2.25%,28)*4400.11 = 90676.71 PV of these annuity payments today = 90676.71/1.0225^4 = 82954.98 PV of the interest payments today = PVAF(2.25%,4)*1500 = 5677.11 PV of future payments on loan = 88632.09 Hence the subsidy = loan disbursed - PV of future payments on loan = 100000 - 88632.09 = \$11,367.91. Question 2 – Time Value of Money (20 marks) Please note: in the following question, parts (a) and (b) are independent, whereas parts (c), (d), and (e) are related. (a) Michael deposits \$500 at the end of each month for the next five years, starting one month from today. After the initial five years, he will reduce his end- of-month deposits to \$250 for another five years. The APR is 6%, monthly compounding. How much money will he accumulate in 10 years? (4 marks) Answer For the first 5 years, the monthly deposit is \$500; in the second 5 years, the monthly contribution is reduced to \$250. The monthly interest rate = APR/12 = 0.06/12 = 0.5%.
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