Question

You are given:

(a) A 10-year 8% semiannual coupon bond is purchased at a discount of X.

(b) A 10-year 9% semiannual coupon bond is purchased at a discount of Y.

(c) A 10-year 10% semiannual coupon bond is purchased at a discount of 0.5X.

(d) All bonds were purchased at the same yield rate, have par values of $1000 and redeemable at par. Calculate Y.

Please use specific math formula TO DO IT instead of using the financial calculator. Thank you!! I will rate it if it's correct. !!

Answer 1

From a)
8%*1000/r*(1-1/(1+r/2)^(2*10))+1000/(1+r/2)^(2*10)=1000-X

From b)
9%*1000/r*(1-1/(1+r/2)^(2*10))+1000/(1+r/2)^(2*10)=1000-Y

From c)
10%*1000/r*(1-1/(1+r/2)^(2*10))+1000/(1+r/2)^(2*10)=1000-0.5X

Subtracting a from c we get
2%*1000/r*(1-1/(1+r/2)^(2*10))=0.5X d)

Substituting in a we get

2X+1000/(1+r/2)^(2*10)=1000-X
=>1000/(1+r/2)^(2*10)=1000-3X e)

Substituting e in d we get
2%*1000/r*(1-(1000-3X)/1000)=0.5X
=>2%*1000/r*(3X/1000)=0.5X
=>2%/r*(3)=0.5
=>r=2%*3/0.5
=>r=12%

X=-(1000/(1+12%/2)^(2*10)-1000)/3=229.3984244

Adding a and c we get
18%*1000/r*(1-1/(1+r/2)^(2*10))+2000/(1+r/2)^(2*10)=2000-1.5X

Dividing by 2 we get
9%*1000/r*(1-1/(1+r/2)^(2*10))+1000/(1+r/2)^(2*10)=1000-0.75X

This is same as b

Hence, Y=0.75X=0.75*229.3984244=172.0488183