You take out an adjustable rate mortgage for $$100,000$ for $20$ years. For the first $5$ years, the rate is $3\%.$ It then rises to $6\%$ for the next $10$ years, and then $8\%$ for the last $5$ years. What are your monthly payments in the first $5$ years, the next $10$ years, and the last $5$ years? $($Assume that each time the rate changes, the payments are recalculated to amortize the remaining debt if the interest rate were to remain constant for the remaining life of the mortgage. Round your answers to the nearest cent.$)$

payments for the first $5$ years

$

payments for the next $10$ years $

payments for the last $5$ years