You Purchase a house for $$400,000$ using a $30$ year adjustable$-$rate mortgage that makes monthly payments with an annualized interest rate of $12\%.$ After $9$ years the interest rate changes to $15\%$ ar after an additional $11$ years the interest rate changes to $3\%.$

$1.$ How much are the monthly mortgage payments under each interest rate $?$

$2.$ Explain how the changes in time, interest rate and principal change the monthly mortgage payments $?$

$($If able to please do this using excel$)$