You purchase a bond that has a par value of $$1,000,$ a coupon rate of $5$ percent, and $7$ years to maturity when the YTM for this bond is $4\mathrm{.}25$ percent. Assume that the bond pays interest annually.

a$.$ What is the price of this bond when you buy it$?$ Use Appendix B and Appendix $D$ to answer the question. Round your answer to the nearest dollar.

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b$.$ If one year elapses and interest rates decrease $75$ basis points, what is the new price of the bond? Use Appendix B and Appendix $D$ to answer the question. Round your answer to the nearest dollar.

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c$.$ What is your rate of return from investing in this bond for the one$-$year period? Round your answer to two decimal places.

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