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.