Assume a borrower purchased a $$100,000$ house with a $$5,000$ down payment and a $30-$year loan with a fixed annual rate of $7\mathrm{.}50\%.$ The lender takes a private mortgage insurance that covers $20$ percent of the loan for the first $10$ years of the loan term. Compute the dollar amount of insurance premium if: a$)$ the premium is $2\mathrm{.}5\%$ of the loan amount and it is paid at closing as a one time premium; b$)$ the premium is $0\mathrm{.}5\%$ of outstanding mortgage balance and it is paid annually as a percentage of remaining loan balance; c$)$ the premium is $0\mathrm{.}05\%$ of outstanding mortgage balance and it is paid monthly as a percentage of remaining loan balance.

These are the answers, please make an excel file able to get these numbers and solve the problem. Please use cell referances.

a$)$ $$2,375$; b$)$ first year$$s premium is $$475,$ second year$$s premium is $$470\mathrm{.}62,$ third year$$s premium is $$465\mathrm{.}90,$ etc.; c$)$ first month$$s premium is $$47\mathrm{.}50,$ second month$$s premium is $$47\mathrm{.}46,$ third month$$s premium is $$47\mathrm{.}43,$ etc.