Mathematics of Investment Assignment | Essay Help Services

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1. Lori borrows 10,000 for 10 years at an effective annual interest rate of 9%. At the end of
each year, she pays the interest on the loan and deposits the level amount necessary to
repay the principle to a sinking fund earning an effective annual rate of 8%. The sum of
the total payments made by Lori over the 10-year period is X. Calculate X.
A) 15,803 B). 15,853 C) 15,903 D). 15,953 E) 16,003
2. William invests 4,000 in a fund. Six months later, he invests 3,000 in the same fund. One
year from the date of the first investment, the fund has grown to 10,000. The fund’s
rate of return is X per year compounded semiannually. Find X.
A) 2.5% B) 5% C) 25% D) 50% E) 100%
3. Bill borrows $330,000 to buy a new home. The terms of the loan are 15 years with equal
monthly payments. Let i (12) = 3%. Calculate the principle repaid with the 23 rd payment.
A) 1524 B) 1528 C) 1532 D) 1536 E) 1540
4. A 10-year bond with a face value of 10,000 makes quarterly payments with an annual
coupon rate of 6%. The bond is selling for 11,642. Calculate the YTM of the bond.
A) .036 B) .038 C) .040 D) .042 E) .044
5. Consider a bond that makes annual coupon payments. Let the face value = 1000, the
coupon rate = 10%, the YTM = 5%, and the time to maturity equals 2 years. Calculate the
modified duration of the bond.
A) 2.032 B) 1.954 C) 1.934 D) 1.902 E) 1.838
6. Let the price of company X stock at the beginning of the year = $100. Assume the stock
is sold short at the beginning of the year and the short sale is closed at the end of the
year at a price of $102. Assume the stock pays a dividend of $2 at the end of the year.
Let the margin requirement = 40%. If the net return on the short sale = 0%, calculate the
rate of return on the margin account.
A) .09 B) .10 C) .11 D) .12 E) .13
7. A project requires an investment of 20,000 now and another investment of 12,000
t years from now. The project will return 5,000 at the end of each of years 2 through 9.
At an effective annual rate of 6%, this project has a net present value of 0. Calculate t.
A) 4.1 B) 4.2 C) 4.3 D) 4.4 E) 4.5
8. A loan of 1000 is made at an interest rate of 12% compounded quarterly. The loan is to
be repaid with three payments: 400 at the end of the first year, 800 at the end of the
fifth year, and the balance at the end of the tenth year. Calculate the amount of the
final payment.
A) 487 B) 587 C) 658 D) 737 E) 812
9. An asset pays $20 today. It then pays $10 at the end of year one with payments
decreasing by $1 per year until the end of year 10. It then pays a perpetuity with a
payment of $15 at the end of year 11 with each subsequent payment growing by 3%
annually. If the annual effective discount rate equals 6.5%, calculate the present value of
the asset.
10. Consider a 15-year loan which is repaid with annual payments, the first payment made
at the end of year one. The annual effective interest rate equals 7%. The amount of
principal repaid in the 5 th payment equals $187. What is the original loan amount?
11. An association had a fund balance of 80,000 on Jan 1, 2019 and a balance of 75,000 on
Dec 31, 2019. At the end of every other month, starting at the end of Feb, the
association deposited 20,000 from membership fees. There were withdrawals of 15,000
made on March 31, 30,000 on June 15, and 90,000 on October 31. Calculate the
dollar-weighted rate of return for the year.
12. Assume there is a coupon bond with a spot price of 1020. Assume the bond pays annual
coupons of 60 with the next coupon to be paid in one year. Let the risk-free rate = 8%.
a. Calculate the delivery price F 0,T for a one year forward contract on the bond with
delivery immediately after the coupon payment is made.
b. After 6 months, the bond price has increased to 1050. Calculate the value of the long
position in the forward contract at t=0.5.
13. You are given the following information with respect to a bond: Face and redemption
value = 1000, term to maturity = 3 years, annual coupon rates = 5% payable annually.
Assume the one-year spot rate = 5%, the two year spot rate = 6%, and the three year
spot rate = 7%. Calculate the yield to maturity on the bond.
A) 6.63 B) 6.73 C) 6.83 D). 6.93 E) 7.03
14. Consider the following information on AJAX Corporation
Bonds: 3,000 8% coupon bonds selling at par value $1,000.
Common stock: 35,000 shares outstanding, selling for $80 per share. Most recent
dividend equals $4.
Preferred stock: 20,000 shares of preferred stock with an annual dividend payment of $6
and a price of $60.
Dividend information on the common stock for a 4-year recent period is as follows:
year 1: D=2.50; year 2: D = 2.60; year 3: D = 2.75; year 4: D = 2.80.
Beta = 1.1
Risk-free rate = 6%
Market return = 14%
Corporate tax rate = 30%
Using the above information calculate the weighted cost of capital for AJAX Corporation.
Be sure to calculate the return on equity using an average of two different stock price
models.
15. The price of XYZ Corporation stock will be either $20 or $50 at the end of one year. XYZ
has a call option available with one year to expiration. The risk free rate is 5%. Let the
current price of XYZ stock = $30 and assume the exercise price of the call option equals
$35. Calculate the value today of the call option on XYZ stock.