Question

1.The spot rate of interest is defined by s(t) = .1(.9)t for t = 1, 2, 3, 4, 5. Find the present value of a 5-year annuity-due in which the first payment is equal to $1000, and each subsequent payment increases by 5% of the immediately preceding payment.

2.You are given the following term structure of spot interest rates:

Term (in years) Spot interest rate

1 5%

2 5.75%

3 6.25%

4 6.50%

A three-year annuity-immediate will be issued a year from now with annual payments of 5000. Using the forward rates, calculate the present value of this annuity a year from now.

Answer #1

1)

s(t) = .1(.9)t

s1 = 0.1*0.9*1 = 0.09

s2 = 0.1*0.9*2 = 0.18

s3 = 0.1*0.9*3 = 0.27

s4 = 0.1*0.9*4 = 0.36

s5 = 0.1*0.9*5 = 0.45

payment at the begining of year 2 = p1 = 1000*1.05 = 1050

payment at the begining of year 3 = p2 = 1050*1.05 = 1102.5

payment at the begining of year 4 = p3 = 1102.5*1.05 = 1157.625

payment at the begining of year 5 = p4 = 1157.625*1.05 = 1215.50625

present value = 1000 + p1/(1+s1) + p2/(1+s2)^{2} +
p3/(1+s3)^{3} + p4/(1+s4)^{4} = 1000 + (1050/1.09)
+ (1102.5/(1.18)^{2}) + (1157.625/(1.27)^{3}) +
(1215.50625/(1.36)^{4})

= 1000 + 963.3027 + 791.7983 + 565.1408 + 355.3051 = $3675.5471 or $3675.56 ( after rounding off to 2 decimal places)

Consider the following spot and forward rates:
1 year spot rate = 4%
3 year spot rate = 5%
4 year forward rate 1 year from now= 6%
Calculate:
2 year forward rate 1 year from now?
2 year forward rate 3 year
Hint: Draw the timeline, plot the given rates
to the corresponding intervals and calculate the forward rate for
the blank interval.

The current 2-year spot rate is 4% and current 5-year spot rate
is 5.5%. According to the pure expectation theory of the term
structure of interest rates, what is the forward rate for 1-year
securities beginning three years from today?
A) 6.44%
B) 7.79%
C) 8.23%
D) 9.58%

The Term Structure
shows the following Spot Rates:
Maturity in years
1
2
3
4
5
spot rate in %
1.8
2.1
2.6
3.2
3.5
What is the implied 2-year forward rate two years from now? What
is the implied 3-year forward rate two years from now?

Consider the forward interest rates defined by the following
equation: fk = 0.09 + 0.002k − 0.002k^2 for k = 0, 1, 2, 3, 4.
1) Find the 4-year spot rate
2) ) Find the 2 year deferred 3-year forward rate.

A 1-year spot rate is 5% today. If the expected future 1-year
spot rate from 2 years from now is 6%, what is the possible forward
rate between year 2 and year 3? Assume the Expectations Hypothesis
holds.
A. 4%
B. 5%
C. 6%
D. 7%
E. None of the above

Suppose that the current 1-year rate (1-year spot rate) and
expected 1-year T-bill rates over the following three years (i.e.,
years 2, 3, and 4, respectively) are as follows: 1R1 = 1%, E(2r1) =
4.25%, E(3r1) = 4.75%, E(4r1) = 6.25% Using the unbiased
expectations theory, calculate the current (longterm) rates for 1-,
2-, 3-, and 4-year-maturity Treasury securities. Plot the resulting
yield curve. (Do not round intermediate calculations. Round your
answers to 2 decimal places.)

Estimate term structure of discount factors, spot rates and
forward rates by using data on five semi-annual coupon paying bonds
with $100 face value each: The bonds, respectively, have 1.25,
5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at annual
rates of 4.35, 5.25, 6.25, 7.25, and 8.25 percent of face value;
and are trading at quoted spot market prices in dollars of 98.25,
99.25, 100.25, 101.25 and 102.25 . Specify the discount factor
function d(t) by a...

Given the following table of spot rates, find the forward rate
for a two year investment beginning 3 years from now.
Spot rate
1 year
2.148%
2 year
3.974%
3 year
4.894%
4 year
5.237%
5 year
5.511%

Suppose that the current 1-year rate (1-year spot rate) and
expected 1-year T-bill rates over the following three years (i.e.,
years 2, 3, and 4, respectively) are as follows:
1R1 = 6%,
E(2r1) = 7%,
E(3r1) = 7.60%,
E(4r1) = 7.95%
Using the unbiased expectations theory, calculate the current
(long-term) rates for 1-, 2-, 3-, and 4-year-maturity Treasury
securities. (Round your answers to 2 decimal
places.)

Assume the following information:
Current spot rate of Australian dollar
=
$.86
Forecasted spot rate of Australian dollar 1 year from now
=
$.88
1-year forward rate of Australian dollar
=
$.93
Annual interest rate for Australian dollar deposit
=
4%
Annual interest rate in the U.S.
=
2%
What is your percentage return from covered interest arbitrage
with $550,000 for one year?

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