A couple wants to save for their daughter's college expense. The daughter will enter college

eight years from now, and she will need $$50,000,$ $$51,000,$ $$52,000,$ and $$53,000$ in actual

dollars for four school years. Assume that these college payments will be made at the beginning

of each school year. The future general inflation rate is estimated to be $7\%$ per year, and the

annual inflation$-$free interest rate is $6\%.$

$($a$)$ What is the market interest rate to use in the analysis?

$($b$)$ What is the equal amount, in actual dollars, the couple must save each year until their

daughter goes to college?