Problem $9-45($Algo$)$ Annuity with changing interest rates $[$LO$9-4]$

You are chairperson of the investment fund for the Continental Soccer League. You are asked to set up a fund of semiannual payments to be compounded semiannually to accumulate a sum of $$260,000$ after ten years at a $12$ percent annual rate $(20$ payments$).$ The first payment into the fund is to take place six months from today, and the last payment is to take place at the end of the tenth year. Use Appendix A and Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

Determine how much the semiannual payment should be$.$

Note: Do not round intermediate calculations. Round your final answer to $2$ decimal places.

On the day after the sixth payment is made $($the beginning of the fourth year$),$ the interest rate goes up to an annual rate of $14$ percent. This new rate applies to the funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded semiannually on all funds.

Determine how much the revised semiannual payments should be after this rate change $($there are $14$ payments and compounding dates$).$ The next payment will be in the middle of the fourth year.

Note: Do not round intermediate calculations. Round your final answer to $2$ decimal places.