Document Preview: Intermediate Macroeconomics
Fall 2012, Homework # 3
Guillaume Vandenbroucke
University of Southern California
Due in class November 12, 2012
1. (4 pts) Suppose the interest rate for a one-period bond is 4%.
(a) What is the price of an asset paying (1,1,1) which means 1 after 1 period, 1 after
2 periods, and 1 after 3 periods.
(b) What is the price of an asset paying (1.5,0,1.5)?
(c) What is the price of an asset paying (0,0,3)?
(d) What is the price of an asset paying (0,0,3,0,0,3,0,0,3)?
2. (4 pts) Suppose the interest rate for a one-period bond is 4% between the current
period and the next. Then the rate becomes 5% for ever.
(a) What is the price of an asset paying (1,1,1) which means 1 after 1 period, 1 after
2 periods, and 1 after 3 periods.
(b) What is the price of an asset paying (1.5,0,1.5)?
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(c) What is the price of an asset paying (0,0,3)?
(d) What is the price of an asset paying (0,0,3,0,0,3,0,0,3)?
3. (3 pts) Suppose that the one-period rate is 4%. Explain why a two-period rate of 6%
cannot be an equilibrium when individuals expect the one-period rate to remain
constant.
4. (3 pts) Suppose that the one-period rate is 4% and that the two-period rate is 6%.
What sort of expectation for the one-period rate next period makes this situation
an equilibrium?
5. (3 pts) Consider an asset paying 1 next period and 2 in two periods. Suppose that
the one-period rate is 4% and that it will remain constant. Show that a price of 2.5
is not an equilibrium price for this asset.
6. (5 pts) Suppose that the annual rate of interest is 4%.
(a) What is the monthly rate?
(b) Consider a 3-year lease on a car that is worth $20,000 today. The ?rst payment
on the lease is next month. After 3 years the price of the car is estimated at
$15,000. What is the monthly rent?
Guillaume Vandenbroucke 2
USC, Los Angeles