A retiree wants to purchase an annuity that will provide her with end$-$of$-$year payments for the next $30$ years. She wants the first annual payment to be $$15,000,$ and for the payments to grow by $3\%$ each year thereafter. If she can earn $5\mathrm{.}5\%$ compounded annually on her investments, what is the purchase price of the annuity today? $($Round your final answer to $2$ decimal places.$)$

Purchase price

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