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?