202 Fall 10, PS 2 Discuss

# 202 Fall 10, PS 2 Discuss - ECO 202 Lyons PROBLEM SET 2...

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ECO 202, Lyons Fall 2010 PROBLEM SET 2 DISCUSSION SHEET - continued - TEXT, CHAPTER 7 Problem 5: Remember that Joanne is very myopic: her stated objective is to maximize the dollar value of her savings account at the end of five years. a) When the interest rate is zero, Joanne’s choices could result in the following outcomes: Working out of high school: she earns \$20,000 for each of 5 years and spends \$15,000 each year, so earnings are \$100,000 and expenses are \$75,000; thus her savings at the end of the period are \$25,000. If she goes to junior college for two years, she earns nothing for two years and \$38,000 for each of the remaining three. She has living expenses of \$75,000 as before, plus college loan costs of \$12,000 for a total of \$87,000. Her income is \$114,000, expenses \$87,000, yielding savings of \$27,000. On a financial basis, she should thus go to junior college. b) If, however, her potential income directly out of high school is \$23,000 per year, she will have \$40,000 in savings at the end of five years rather than the \$27,000 from going to junior college; if her time horizon is only five years then she should go to work immediately. The opportunity cost of going to college in this case is higher than in a), and thus she is less likely to do so. c) The same consideration applies if she must borrow (and repay) \$2,000 more per year, so her savings will be lower after junior college (\$27,000 - \$4,000) = \$23,000, which is less than she would save by going directly to work. d) With a 10% interest rate, Joanne’s annual savings will grow to a larger total at the end of five years, but so will any debt she incurs. If she saves \$5,000 each year by going to work immediately as before, she can earn 4 years of (compound) interest on her first year’s savings, 3 on her second, etc. First year savings at the end of year 5 are \$5,000•(1.10) 4 = \$7,321. Second year savings at the end of year 5 are \$5,000•(1.10) 3 = \$6,655. Following this procedure for each of the other years of savings will yield a total of \$30,526 in her savings account (total interest earned is \$5,526). If she goes to junior college she must borrow to cover both living expenses and college costs. In year 1 she borrows \$21,000 which, at the end of year 5 has grown to \$21,000•(1.10) 4 = \$30,746. She borrows again in year 2, which at the end of year 5 amounts to \$21,000•(1.10) 3 = \$27,951. After beginning work, she saves \$23,000 per year and earns interest, but only for three years. Total savings will be \$23,000 each year for three years, plus 2 years’ compound interest for year 1 savings and 1 year’s interest for year 2 savings, a total of \$76,130.

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