A person takes out a $10, 000 loan at an effective annual interest rate of 2% and can repay the loan with constant payments P at the end of each year for 10 years (starting one year after the loan was made.)

Instead, the person can make deposits into a sinking fund at the end of each year, starting one year after the loan was made. The deposits to the sinking fund are equal to 50% of P minus the yearly interest on the loan. Find when there will be enough in the fund to completely pay off the loan, and how much will be in the fund immediately after the repayment of the loan. Here, the effective annual interest rate for the sinking fund is i = 3%