Cindy borrows $$13,800$ for twelve years at an annual effective interest rate of i$.$ She accumulates the amount necessary to repay the loan by a sinking fund. Cindy makes a payment of P at the end of each of the twelve years of the loan period; each includes payment on the loan at an annual effective interest rate of i and payment into a sinking fund on which the annual effective interest rate is $4\%.$ If the annual effective rate on the loan had been $2$i instead of i$,$ Cindy's total annual payment would have been $1\mathrm{.}3$P$.$ Find the amount P$.($Round your answer to the nearest cent.$)$