Bill buys a 10 year 1000 par value bond with semi-annual coupons paid at an annual rate of 6%. The price assumes an annual nominal yield of 6% compounded semiannually. As Bill receives each coupon payment, he immediately puts the money into an account earning interest at an annual effective rate of i. At the end of 10 years, immediately after Bill receives the final coupon payment and the redemption value of the bond, Bill has earned an annual effective yield rate of 7% on his investment in the bond. Calculate ia. 9.50% b. 9.75% c. 10.00% d. 10.25% e. 10.50%

B. 9.75%

Explanation:

Amount invested by Bill = $1,000

Effective yield = 7% and n = 10 years.

Thus total amount received by Bill at the end of 10 years = 1,000 * (1+7%) ^10 = $1,967.15

This amount is received in 2 parts - part 1 is the principal repayment and part 2 is the accumulated value of coupons.

Value of each coupon = $1000*6%/2 = $30. Total no. of coupons = 10*2 = 20

Let the effective semiannual interest rate be "j" and j = (1+i) ^1/2 - 1

Thus 1000*1.07^10 = 1000+30*S20j

S20j = (1000*1.07^10 - 1000) / 30 = 32.2384

Thus solving the equation 1000*1.07^10 = 1000+30*S20j we get j = 4.7596%

i = (1+j) ^2 - 1

= (1+4.7596%) ^2 - 1

= 9.75%