Based or or using a financial calculator, what would be the monthly mortgage payments for each of the following situations:

Note: Round time value factor and final answers to $2$ decimal places.

What relationship exists between the length of the loan and the monthly payment? How does the mortgage rate affect the monthly payment?

$\backslash$table$[[,\backslash$table$[[$Monthly Mortgage$],[$Payment$]],],[$a$.$ $$119,000,15-$year loan at $6\mathrm{.}00$ percent.,,$],[$b$.$ $$103,000,30-$year loan at $8\mathrm{.}00$ percent.,,$],[$c$.$ $$96,000,20-$year loan at $5\mathrm{.}00$ percent.,,$],[$d$-1.$ Longer mortgage terms mean a$,$Tower,monthly payment.$],[$d$-2.$ For increase in mortgage rate,higher,monthly payment is required.$]]$

$\backslash$table$[[$Term Rate,$30$ years,$25$ years,$20$ years,$15$ years$],[3\mathrm{.}0\%,$$$4\mathrm{.}22,$$$4\mathrm{.}74,$$$5\mathrm{.}55,$$$6\mathrm{.}91$