Renee buys a perpetuity paying $$1,000$ every two years, starting immediately. She deposits the payments into a savings account earning interest at an effective annual interest rate of $3\%.$ Ten years later, before receiving the sixth payment, Renee sells the perpetuity based on an effective annual interest rate of $3\%.$ Using proceeds from the sale plus the money in the savings account, Renee purchases an annuity paying P at the end of every three years for thirty years at an annual effective interest rate of $3\%.$ Find P$.$ Do this problem twice, once using Chapter $3$ methods and once using Section $(4\mathrm{.}2)$ techniques. $($Round your answer to the nearest cent.$)$