You are chairperson of the investment fund for Middle Hockey League. You are asked to set up a fund of quarterly payments to be compounded quarterly to accumulate a sum of $$300,000$ after $10$ years at an $8$ percent annual rate $(40$ payments$).$ The first payment into the fund is to occur three months from today, and the last payment is to take place at the end of the $10$th year. Use Appendix A and Appendix C$.($Round $"$FV Factor" to $3$ decimal places. Round your intermediate calculations to the nearest whole dollars. Round the final answers to the nearest whole dollar.$)$

a$.$ Determine how much the quarterly payment should be$.$

Quarterly payment $

b$.$ On the day after the sixteenth payment is made $($the end of the fourth year$)$ the interest rate goes up to a $12$ percent annual rate, and you can earn a $12$ percent annual rate on funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded quarterly on all funds. Determine how much the revised quarterly payments should be after this rate change $($there are $24$ payments and compounding dates$).$ The next payment will be in the fourth quarter of the fourth year.

Revised quarterly payments $