Econ 161A: Money and Banking
Spring 2017: Jenkins
Assignment #2
Due: Thursday, April 20, 2017
Instructions: You may work with your colleagues, but you must submit your own assignment to receive credit. The assignment is due at the beginning of the class on the the due
date for the assignment. Late assignments must be submitted to your TA within 24 hours
of the due date/time to be eligible for half credit. You may make arrangements with your
TA to submit your assignment early if necessary.
1. You have two relatively small student loans from two different lenders. The loans have
the same principals but different interest rates:
Loan
A
B
Initial balance Interest rate
$4,000
0.04
$4,000
0.06
Interest accrues on the balances annually. Assume that your lenders do not require
you to make a minimum payment each period. You have decided that you can afford
to spend $1,000 per year to pay back these loans. Interest will begin accruing in one
year. In this problem you will compare two repayment options.
(a) First, suppose that you will divide your $1,000 annual payment equally between
the two loans. If one loan happens to be paid off first, then you will allocate
available funds toward the remaining loan. How many years will it take for you
to pay off both loans? What is the cumulative dollar value of the interest that
you will end up paying to your lender?
(b) Now, suppose that you will use all available funds to payoff the higher interest
loan first. Once the higher interest loan is paid off, you will then allocate all
available funds to the lower interest loan. How many years will it take for you to
pay both loans? What is the cumulative dollar value of the interest that you will
end up paying to your lender?
(c) Based on your answers, what do you conclude about the best way to simultaneously pay back multiple loans that have different interest rates?
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2. Answer the following.
(a) A 20-year coupon bond with a face value of $100,000 sells for a price of $65,636.50,
has a yield to maturity of i = 0.08, and makes annual coupon payments. Find
the value of the bond’s annual coupon payment (rounded to the nearest cent) and
the bond’s coupon rate.
(b) A bank makes a fixed payment loan to a student for $50,000. The loan is to be
repaid in 10 annual fixed payments beginning 4 years after the loan is made. That
is, supposing that the loan is made at the beginning of year 0, the fixed payments
F P start at the beginning of year 4 and continue through the beginning of year
13:
Loan made
0
1
2
3
FP
FP
FP
FP
4
5
6
13
If the lender requires a yield to maturity of i = 0.05, what must be the value of
the annual fixed payments?
3. You purchase a 30-year bond today with a $10,000 face value that makes annual coupon
payments at a 5% coupon rate.
(a) If the yield to maturity on 30 year bonds at the time of purchase was 4%, how
much did you pay for the 30 year bond?
(b) After holding the bond for 1 year, you find that the yield to maturity on 29 year
bonds is 5%. What is new price of your bond and what has been the rate of
return from holding
the bond over the first year?1 at the top of the present value
PN
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table to compute k=1 (1+i)
k for i = 0.05 and N = 29.)
(c) After holding the bond for a second year, you find that the yield to maturity on
28 year bonds is 3.5%. What is new price of your bond and what has been the
rate of return from holding the bond from the first year to the second?
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The formula that you need:
N
X
k=1
1
(1 + i)k
=
1 − (1 + i)−N
i
2
(1)
4. Visit FRED (https://fred.stlouisfed.org/) to obtain the yields on the 4-week, 3-month,
and 6-month US T-bills for April 13, 2017.
- 4-Week Treasury Bill: Secondary Market Rate (Daily, Not seasonally Adjusted,
Series ID: DTB4WK, location: Money, Banking, & Finance > Interest Rates >
Treasury Bills)
- 3-Month Treasury Bill: Secondary Market Rate (Daily, Not seasonally Adjusted,
Series ID: DTB3, location: Money, Banking, & Finance > Interest Rates > Treasury Bills)
- 6-Month Treasury Bill: Secondary Market Rate (Daily, Not seasonally Adjusted,
Series ID: DTB6, location: Money, Banking, & Finance > Interest Rates > Treasury Bills)
Answer the following:
(a) Of the three T-bills you obtained, which had the highest yield? Which had the
lowest?
(b) Assuming a $100,000 face value, compute the prices of the 4-week, 3-month, and
6-month T-bills implied by the yields that you found.
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