Question

18. Bill buys a 10-year 1000 par value 6% bond with semi-annual coupons. The price assumes a nominal yield of 6%, compounded semi-annually. 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 of 7% on his investment in the bond. Calculate (A) 9.50% (B) 9.75% (C) 10.00% (D) 10.25% (E) 10.50%

Answer 1

solution toom the given information , we have Amount invested by Bill = $1,000 Effective yield = 7% and n= 10 years Thus total amount received by son of the end of to years = 1,000*(1+77)70=819 This amount as received in a parts - part 1 is the poincipal repaymet and part 2 is the accumulated value of coupe value of each coupon = $1000* 6%/2 = 830 Total no. of couporn 18+ = let the effective semiannual interest rate be 'j 'and j =(1+1) 1/2- Thus 1000*1.07110 = 1000 + 30*530) S205 - (1000*1.07 10-1000)/30 = 32: 2354 Thus solving the equation 100021.07710 = 1000+30* Sici we get j = 4.7596% i = C1 +3)^2-1 =(1+4.75967) "2-1 = 9.757 Answer = option B=9.75%