On January $1,$ the Wiek Company contracted with its president, T$.$ Mae, to make a single deposit immediately to establish a fund with a trustee that pays Mae $$40,000$ per year for each of the three years following retirement. Mae will retire after $10$ years on December $31,$ and the three equal annual payments are to be made by the trustee each December $31$ starting at the end of the $11$th year. The trustee will add to the fund $8\%$ annual compound interest each year$-$end. The fund is to have a zero balance on December $31,$ immediately after the last payment to the president.

How much of the total amount paid to the president during the payout period is provided by interest earned during the three$-$year payout period?