Math 325
Additional Problems – Ch 6,7
1. Tim invests 1000 at the beginning of the year in a fund which credits interest at an annual effective
interest of 7%.
He reinvests each interest payment in a separate fund, earning an annual effective interest rate of 6%.
The interest payments from this fund are put in a bank account where they accumulate at 5% effective.
Compute the accumulated value in all the accounts together, at the end of 10 years.
2. A company invests 1000 at the end of each year for 10 years. Starting at the end of the 11th year, it
receives 1000 at the end of each year in perpetuity. Calculate the company's yield on this transaction.
3.You are given the following information about Chris's stock portfolio:
Date
Fund Values prior to any withdrawals or deposits (in dollars)
1/1/1994
100,000
1/1/1995
115,000
1/1/1996
145,000
1/1/1997
185,000
1/1/1998
100,000
Date
Withdrawals or deposits, immediately after the given dates (in
dollars)
1/1/1994
0
1/1/1995
Deposit : 18,000
1/1/1996
Deposit : 23,000
1/1/1997
Withdrawal : X
1/1/1998
0
If the time-weighted return is 10% annualized, over the 4-year period, find the dollar-weighted return.
4. You are given the following bonds that have a par value of 100
Bond I
Bond II
Coupon Rate
8%, payable semiannually
7%, payable semiannually
Yield Rate
5.5%, effective annually
5.1%, effective annually
Term
10
10
Redemption Value
100
X
Price
Y
0.9Y
Find X.
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Math 325
Additional Problems – Ch 6,7
5. Payments of X are made at the beginning of each year for 20 years. These payments earn an interest
at the end of each year at an annual effective rate of 8%. The interest is immediately reinvested at an
annual effective rate of 6%. At the end of 20 years, the accumulated value of the 20 payments and the
reinvested interest is 5600. Calculate X.
6. Ted received a 5-year $1000 bond with coupons at 6% convertible semiannually. Rob buys a 10-year
bond with face amount X and coupons at 6% convertible semiannually. Both the bonds are redeemable
at par.
Ted and Rob buy their bonds to yield 4% compounded semiannually and immediately sell them to an
investor who will yield 2% compounded semiannually. Both make the same profit.
Compute X.
7. Dave purchases a 1000 par value 10-year bond with 8% semiannual coupons for 850.He is able to
reinvest the coupon payments at a nominal rate of 6% convertible semiannually. Calculate his nominal
annual yield rate convertible semiannually over the 10-yr period.
8. 1000 is deposited into Fund X, which earns an annual effective rate of 6%. At the end of each year,
the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the
fund is depleted.
The annual withdrawals of interest and principal are deposited into a Fund Y, which earns an annual
interest of 9%.
Calculate the accumulated value of Fund Y a the end of 10 years.
9. A 15-year 8% bond with a face amount of 100 is callable on a coupon date in the 10th to 15th years. In
the 10th year, the bond is callable at par, in the 11th and 12th yeas at 115, or in the 13th, 14th or 15th years
at redemption amount 135.
What price should an investor pay in order to ensure a minimum nominal yield to maturity of
a) 12%
b) 6%
10. Consider a $100 par value 4% bond with semiannual coupons callable at $109 on any coupon date
starting 5 years after issue for the next 5 years, at $104.50 starting 10 years after issue for the next 5
years, and maturing at $100 at the end of 15 years. Find the highest price which an investor can pay and
still be certain of a yield of
a) 5% convertible semiannually
b) 3% convertible semiannually
11. A 20year bond with 10% coupons paid semiannually, is redeemable at par. The bond's annual
effective yield is 8%. Calculate the amount of premium amortized in the 11th coupon payment.
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Math 325
Additional Problems – Ch 6,7
12. A corporate bond pays semiannual coupons at a rate of 8%. The bond is priced to yield 6%
compounded semiannually. The bond matures on 6/1/08 and is purchased with a settlement date of
10/1/03. Determine the full price and and accrued interest of the bond as of the settlement date.
13. A 15-year bond with a face amount of $100 pays semiannual coupons of 4% per year and is
redeemable at $105. The bond is priced to yield 5% per year, convertible semiannually.
a) Determine the price of the bond.
b) Determine the book value of the bond immediately after the 10th coupon payment.
c) Determine the amount of discount accumulated in the 11th coupon payment.
14. For a certain bond that pays semiannual coupons, the amount of premium amortized in the 10th
payment is $0.305135 and the amount of premium amortized in the 15th payment is $0.345233.
Determine the bond’s annual effective yield.
15. You are given the following table of interest rates:
Calendar Year of
Original Investment,
y
Investment Year Rates (in %)
iy
1
i
2
y
iy
3
i
4
y
Portfolio Rates
(in %)
iy
i y+5
5
1992
8.25
8.25
8.40
8.50
8.50
8.35
1993
8.50
8.70
8.75
8.90
9.00
8.60
1994
9.00
9.00
9.10
9.10
9.20
8.85
1995
9.00
9.10
9.20
9.30
9.40
9.10
1996
9.25
9.35
9.50
9.55
9.60
9.35
1997
9.50
9.50
9.60
9.70
9.70
1998
10.00
10.00
9.90
9.80
1999
10.00
9.80
9.70
2000
9.50
9.50
2001
9.00
The amount in the fund on January 1, 1997 is $1000. Let the following be the accumulated value of the
fund on Jan 1, 2001:
P: under the investment year method
Q: under the portfolio method
R: if the balance is withdrawn at the end of every year and is reinvested at the new money rate.
Determine P, Q, and R.
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