Question $3$: Assume an ARM for $$100,000$ with an initial interest rate of $6\%$ with a term of $30$ years with payments being reset at the end of each year based on an index. The ARM is subject to a payment cap of $10\%.$ If the market index were to rise at the end of the first year and it changes the interest rate on the ARM to $8\%,$ what would be the new monthly payment amount?