QUESTION : A 20-year Bond was issued at par value of $1000 with a 7.5% per year

Question

QUESTION: A 20-year Bond was issued at par value of $1000 with a 7.5% per year coupon rate. Coupon interest payments are made semi-annually. Two years after issuance, the Bond sold for $965.

A. What should the market price of the bond be four years after issuance if the current market interest rate for comparably rated bonds is 12% per year compounded semi-annually? (Assume the seller recieves the coupon payment at the end of four years before the sale)

B. Six years after issuance the bond sells for $1060. What is the current yield of the bond at that price and time in terms of rate per 1/2 year (6 months) AND efective rate per year?

This Question is for an Engineering Economy Class, and was given during a practice test.. Please answer in detail, with steps shown. I'm not looking for an EXCEL answer, as during our tests we won't have a computer. I will thumbs down any excel answer as that is NOT what I'm asking for. Thank you for your help.

Explanation / Answer

Coupons=7.5%*1000/2=37.5

Price after 4 years=37.5/1.06+37.5/1.06^2.....................37.5/1.06^32+1000/1.06^32

=37.5/1.06*(1-1/1.06^32)/(1-1/1.06)+1000/1.06^32

=37.5/0.06*(1-1/1.06^32)+1000/1.06^32

=683.109

Price after 6 years=37.5/(1+r)+37.5/(1+r/2)^2.....................37.5/(1+r/2)^28+1000/(1+r/2)^28

=37.5/(1+r/2)*(1-1/(1+r/2)^28)/(1-1/(1+r/2))+1000/(1+r/2)^28

=37.5*2/r*(1-1/(1+r/2)^28)+1000/(1+r/2)^28

Hence, 1060=37.5*2/r*(1-1/(1+r/2)^28)+1000/(1+r/2)^28

=>r=6.8277% effective rate per year

half yearly rate=1.068277^0.5-1=3.3575%

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