Question

19 and 20

19-Angelina has planned to start her college education four years from now. To pay for her college education, she has decided to save $1.000 each quarter for the next four years in a bank account paying 12 percent interest. How much will she have at the end of the fourth year? 20- The XYZ Company's bonds have a face value of $1,000, will mature in ten years, and carry a coupon rate of 12 percent. Assume interest payments are made semi-annually. a. Determine the present value of the bond's price if the required rate of return is 12 percent b. How would your answer change if the required rate of return is 10 percent? c. How would your answer change if the required return is 16 percent?

Answer 1

Answer to Question 19:

Quarterly deposit = $1,000
Number of deposits = 16 (4 years)
Annual interest rate = 12%
Quarterly interest rate = 3%

Accumulated sum = $1,000*1.03^15 + $1,000*1.03^14 + … + $1,000*1.03 + $1,000
Accumulated sum = $1,000 * (1.03^16 - 1) / 0.03
Accumulated sum = $1,000 * 20.15688
Accumulated sum = $20,156.88

Answer to Question 20:

Face value = $1,000

Annual coupon rate = 12%
Semiannual coupon rate = 6%
Semiannual coupon = 6% * $1,000
Semiannual coupon = $60

Time to maturity = 10 years
Semiannual period = 20

Part a:

Annual required return = 12%
Semiannual required return = 6%

Present value = $60 * PVIFA(6%, 20) + $1,000 * PVIF(6%, 20)
Present value = $60 * (1 - (1/1.06)^20) / 0.06 + $1,000 / 1.06^20
Present value = $1,000.00

Part b:

Annual required return = 10%
Semiannual required return = 5%

Present value = $60 * PVIFA(5%, 20) + $1,000 * PVIF(5%, 20)
Present value = $60 * (1 - (1/1.05)^20) / 0.05 + $1,000 / 1.05^20
Present value = $1,124.62

Part c:

Annual required return = 16%
Semiannual required return = 8%

Present value = $60 * PVIFA(8%, 20) + $1,000 * PVIF(8%, 20)
Present value = $60 * (1 - (1/1.08)^20) / 0.08 + $1,000 / 1.08^20
Present value = $803.64