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azamat
2 months ago
10

A bond has a face value of $1,000, a coupon of 4% paid annually, a maturity of 30 years, and a yield to maturity of 7%. What rat

e of return will be earned by an investor who purchases the bond for $627.73 and holds it for 1 year if the bond’s yield to maturity at the end of the year is 8%?
Business
1 answer:
Scilla [3.8K]2 months ago
4 0

Response:

-11.8%

Clarification:

to resolve this problem, it's important to keep in mind that a bond's worth is primarily determined by figuring out the present value of its cash flow sequence. Therefore, consider a bond in terms of you being the creditor; you would earn interest from the loaned amount (the coupon), and after n years, you'd receive back the initial amount lent (the principal). Applying the relevant formula, we get the value of the bond as follows:

price=\frac{principal*coupon}{(1+i)^{1} }+ \frac{principal*coupon}{(1+i)^{2} } \frac{principal*coupon}{(1+i)^{3} }+...+\frac{principal+principal*coupon}{(1+i)^{n} }

in this specific scenario, there are 29 years left until it matures after one year, thus we have:

price=\frac{1,000*0.04}{(1+0.08)^{1} }+ \frac{1,000*0.04}{(1+0.08)^{2} } \frac{1000*0.04}{(1+0.08)^{3} }+...+\frac{1,000+1,000*0.04}{(1+0.08)^{30} }

price=553.6638

given that the interest rate is higher, the return on the investment is as follows:

return=\frac{553.66}{627.73} -1

return=-11.8\%

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