Bill enters an agreement that requires him to pay $$50,000$ today in exchange for $25,000$ in three years and $$35000$ in $6$ years.

a$.)$ Compute Bill$$s net present value if the annual effective rate of interest is $5\%.$

b$.)$ Compute Bill$$s annual effective yield rate.

c$.)$ What is Bill$$s annual effective yield rate if he receives an additional $$2000$ after $4$ years?