Assume an elderly couple owns a $$140,000$ home that is free and clear of mortgage debt.

A reverse annuity mortgage $($RAM$)$ lender has agreed to a $$100,000$ RAM. The loan term

is $12$ years, the contract is $9\mathrm{.}25\%,$ and payments will be made at the end of each month.

a$.$ What is the monthly payment on this RAM?

b$.$ Fill in the following partial loan amortization table:

c$.$ What will be the loan balance at the end of the $12-$year term?

d$.$ What portion of the loan balance at the end of year $12$ represents principal? What

portion represents interest?