1. You have an adjustable-rate mortgage (ARM) with the following characteristics: Mortgage Amount: $200,000 Initial Rate: 5% Initial fixed rate period: 3 years Life time cap: 5% Periodic cap: 2% Margin: 3\% Index: SOFR Term: 30 years Monthly payments After the initial fixed rate period, the ARM rate and payment can adjust every year. Assume the SOFR index is the following for the next 30 years \begin{tabular}{|c|c|} \hline & SOFR \\ Year & 3% \\ \hline 13 & 5% \\ \hline 4 & 5% \\ \hline 5 & 3% \\ \hline 630 & \\ \hline \end{tabular} 1a. What is the initial monthly mortgage payment? 1b. What is the outstanding balance of the mortgage at the end of year 3 ? 1c. What will the mortgage rate at the beginning of month 37 ? 1d. What will be the mortgage payment in month 37