Abond 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 rate 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%?

-11.8%

Explanation:

the key to answer this question is to remember that valuation of a bond depends basically of calculating the present value of a series of cash flows, so let´s think about a bond as if you were a lender so you will get interest by the money you lend (coupon) and at the end of n years you will get back the money you lend at the beginnin (principal), so applying math we have the bond value given by:

so in this particular case that one year later there are 29 years to maturity so we have:

so as we have a higher rate the investment has the next return:

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