Assignment
raa.o
assignment_1_2012.docAssignment 1 for Unit 2.
You have to SHOW your work (show how you get the answers) to get credit. The answers to these problems are given to you on a separate file.
Below are the formulas for each type of loan and bonds. Use the respective formula regarding a respective question: for example, on questions regarding a simple loan use the simple loan formula, on questions regarding a fixed payment loan question use the fixed payment loan formula, and so on.
You also have to know the formulas for the test.
Future Value :
F
C
rate
coupon
=
FV= future value, PV= present value, i= interest rate, N= number of years.
.
Present Value:
(1)
N
FV
PV
i
=
+
FV= future value, PV= present value, i= interest rate, N= number of years.
Simple loan:
(1)
N
FVPVi
=+
FV = future value, i = interest rate, n = number of years
Fixed payment loan:
n
i
FV
loan
)
1
(
+
=
FP = fixed payment, i = interest rate, n = number of years
n
i
FP
i
FP
i
FP
loan
)
1
(
...
)
1
(
)
1
(
2
1
+
+
+
+
+
+
=
Coupon bond:P = price of bond, i = interest rate, n = number of years, c = coupon payment, and F = face value of the bond.
n
i
F
C
i
C
i
C
P
)
1
(
...
)
1
(
)
1
(
2
1
+
+
+
+
+
+
+
=
P = price of bond, C = coupon payment
P
C
yield
current
=
F = face value, C = coupon payment
Discount Bond:
F
C
rate
coupon
=
P = price of bond, i = interest rate, n = number of years, F = face value
Yield to maturity on a discount bond with less than a year of maturity:
n
i
F
P
)
1
(
+
=
P = price of bond, F = Face value, G = number of days to maturity.
Yield on discount basis on a bond with less than a year of maturity:
G
P
P
F
ytm
365
*
-
=
P = price of bond, F = face value
G
F
P
F
basis
discount
on
yield
360
*
-
=
Consol bond:P = price of bond, i = interest rate
Bring the answers to the following questions to Class
simple loan:
1. End of ten years you will pay back $20,000. If I = 6% , how much is the loan amount now.
2. If you borrowed $9900 at i = 10% to pay back at the end of 15 years, how much money do you pay back?
3. You will receive $35,000 at the end of two years. Its present value is $20,000. The yield to maturity equals what?
fixed payment loan:
1. i = 9%, loan = $15,000, 5 year loan. The fixed payment =___.
2. The fixed payment = $7000,
i. i= 9%, 3 years, loan =___
coupon bond:
1. coupon payment = $100, face value = $6000, i = 5%, 4 years, a) price of bond =___ b) coupon rate =___ c) current yield =____
2. Coupon rate = 5%, face value = $12,000, i = 7% a) price of bond for a) 1 year bond=___, b) 2 year bond =____ c) 3 year bond =_____
3. if i increases to 12% , what happens to each of the prices (in a) above.
discount bond (zero coupon bond):
1. Face value = $20,000, price = $19,000, 1 year bond, ytm = _
2. Face value = $20,000, price 19,000, 1 year bond , number of days to maturity = 90 days. a) ytm =_______ b) yield on discount basis =___
3. Face value = $15,000, 1 year bond, ytm = 6%, number of days to maturity = 180 days. A) price of bond =_______ b) yield on discount basis =___
console bond:
1. i = 7%, price of bond = $15,000. coupon payment = _
2. Coupon payment = $200,000 , i = 7%, price of bond =__
3. Price of bond = $50,000 coupon payment = $300, ytm = __
Other Problems
1. average interest rate equals 6%, You promised some one to pay her/him $10,000 at the end of 20 years. If the person insist to paid cash now how much should you give her/him now?
2. Let’s say I am supposed to give you $12,000 at the end of 5 years, $16,000 at the end of 7 years, and another $15,000 at the end of 9 years. If the average rate of interest is 6% and you want to get your money now instead of waiting, how much should I give you?
3. If the average rate of interest is 5%, and you want to receive $15,000 a year from a trust fund, how much money should you put in the trust fund?
4. If the average rate of interest is 5%, and you deposit $2,000 a year during the coming 3 years how much money would you have at the end of the 3RD year?.
5. If average interest rate is 7%, and tuition is currently $6,000 a year, how much would it be at the end of 3 years?
6. You want your mother to receive $60,000 per year, if the average rate of interest is 5.5%, how much money should you put in a trust fund so your mother would get $60,000 per year?
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i
C
P
=
n
i
FV
loan
)
1
(
+
=
n
i
FP
i
FP
i
FP
loan
)
1
(
...
)
1
(
)
1
(
2
1
+
+
+
+
+
+
=
n
i
F
C
i
C
i
C
P
)
1
(
...
)
1
(
)
1
(
2
1
+
+
+
+
+
+
+
=
n
i
F
P
)
1
(
+
=
G
P
P
F
ytm
365
*
-
=
i
C
P
=
G
F
P
F
basis
discount
on
yield
360
*
-
=
P
C
yield
current
=
