Question

the possible answers are 2%,3%,4%,5%,6%

27. On January 1, 1987, three 100 par value bonds with 6% annual coupons will mature at the end of 1, 2, and 3 years, respectively. The redemption value of each bond is 100. You are given that the prices for these bonds on January 1, 1987 are: Maturity Date Price December 31, 1987 101.92 December 31, 1988 102.84 December 31, 1989 105.51 These prices are based on an interest rate of i in 1987, j in 1988, and k in 1989. Determine j.

Answer 1

(100+6%*100)/(1+i)=101.92
=>i=(100+6%*100)/101.92-1
=>i=4.00%

100*6%/1.04+(100+6%*100)/(1+j)^2=102.84
=>j=((100+6%*100)/(102.84-100*6%/1.04))^(1/2)-1
=>j=4.50%

100*6%/1.04+100*6%/1.045^2+(100+6%*100)/(1+k)^3=105.51
=>k=((100+6%*100)/(103.51-100*6%/1.04-100*6%/1.045^2))^(1/3)-1
=>k=4.74%