A mortgage loan in the amount of $$112,000$ is made at $6$ percent interest $($compounded

monthly$)$ for $20$ years. If the borrower and lender agree that the loan balance of $$186,000$ will be payable at the end of year $20.$ Payments are to be monthly.

a$.$ How much total interest will be paid from all payments? How much total principal

will be paid?

b$.$ What will be the loan balance at the end of year $3?$

c$.$ If the loan is repaid at the end of year $3,$ what will be the effective rate of interest?

$($Use Excel to compute the monthly interest rate$).$

d$.$ If the lender charges $4$ points to make this loan, what will the effective rate of interest

be if the loan is repaid at the end of year $3?($Use Excel to compute the monthly

interest rate$).$