Consider a lottery that pays to the winner an annual annuity of $$80$ that begins in one year and continues for $8$ consecutive years with one exception $--$ the payment at the end of year $3($and only in this year$)$ is not $$80$ but instead is $$120.$ Using an interest rate of $5\%,$ determine the present value of this prize.

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Place your answer in dollars and cents without using a dollar sign or a comma. For example, if your answer is one hundred thousand five hundred and seventy then place your answer as $100570.$ Work all analysis using at least four decimal places of accuracy.