For each of the following investments, indicate the equation Kim should use to calculate the yield to maturity.

a$)$ Kim takes out a $5$ year mortgage to purchase a $$260,000$ house. The annual mortgage payment is $$20,000$ with an additional rupfront payment of $$6,500.$

b$)$ Kim pays $$1,400$ for a perpetuity with an annual coupon of $$20.$

c$)$ Kim pays $$250$ for a $4$ year coupon bond with a $$4,900$ face value and $2\%$ coupon rate.