1
DEPARTMENT OF ECONOMICS
Econ 500 – Money and Banking
Fall 2011
Assignment 2 – Answer Key
1.
Chapter 4, Q8 from textbook: To pay for college, you have just taken out a $1000
government loan that makes you pay $126 per year for 25 years.
However, you do not have
to start making payments until you graduate from college
TWO years from today
.
Why is
the yield to maturity (TODAY) necessarily LESS than 12%? (Hint: remember that the yield
to maturity (TODAY)
is exactly 12% on a normal (standard) $1000 fixed payment loan, in
which you pay $126 per year for 25years starting next year).
Recall, that if the
PV of X = Y, then X>Y; and the further the future payment, the bigger the
difference between X and Y, for a given interest rate. (Just look at question 5)!
Hence, if the Loan
to be repaid is $1000, and the payments are $126, the further the payment is in the future (given
i=10%) the lower the PV of that future payments.
Hence, if the payments are postponed, then the
PV (i.e. the sum of all those payments) of the loan is going to be smaller for i=10%, and will not
equal $1000.
In that case, i has to fall in order for the PV to increase to $1000.
So, i is smaller than
$1000.
Another Way to see the answer to Question 7 is (a bit long) but hopefully clear:
Suppose you did start to pay next year.
Then the PV is
(1)
2
25
FP
FP
FP
PV
....
(1
i)
(1
i)
(1
i)
Get yield to maturity by setting PV=LV
2
25
126
126
126
1000
....
(1
i)
(1
i)
(1
i)
From chapter 4 (text) we know that in this case i = 12%.
Now if I start paying 2 years from now not 1 year from now the PV is
Econ 500
Fall 2011
Z. Janko

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2
(2)
2
3
26
126
126
126
PV
....
(1
i)
(1
i)
(1
i)
note that n = years to maturity is still 25
NOW LETS COMPARE THE PRESENT VALUE IN EQUATION 1 AND THE PRESENT
VALUE IN EQUATION 2
2
25
126
126
126
PV1
....
(1
i)
(1
i)
(1
i)
2
3
25
26
126
126
126
126
PV2
....
(1
i)
(1
i)
(1
i)
1
i
The difference between the two is :
PV1 has
126
(1
i)
but does not have
26
126
(1
i)
PV2 has
26
126
(1
i)
but does not have
126
(1
i)
Question:
If i=12% which term is bigger:
126
(1
i)
or
26
126
(1
i)
?

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