Consider a bond being sold in the primary market with the following characteristics:

currently priced at $$1,000$ which has $3$ years to maturity, a $6\%$ annual coupon rate, and a face value of

$$1,000$ at maturity.

a$.$ What is the yield to maturity of the bond? Please explain for full credit.

b$.$ Suppose that one year after you buy the bond, the interest rate increases $3\%$ from the interest rate

last year. If you decide to sell the bond then, what is your rate of return?

please do all steps and show work and explanation will upvote