X is buying a fixed interest mortgage for a home listed at USD $80000$

X is interested in comparing the effects of a

$10\%$ versus a $20\%$down payment option on monthly mortgage payments, the total interest paid over the life of the mortgage, the total interest paid over the life of the mortgage, and long$-$term financial implications including the requirement for insurance premium.

Prepare a detailed analysis for X$,$ examining the two down payment options for a $25-$year fixed$-$ rate mortgage with an interest rate of $3\mathrm{.}75\%.$ Please answer the following questions with above key points:

A$.$ Total Interest Paid by X

a$.$ Determine the total interest paid over the life of the mortgage for each scenario.

B$.$ Insurance Premiums :

a$.$ Cost of insurance premium for $10\%$ scenario only is $$257\mathrm{.}26$ Mortgage amount is $$74232$ interest cost is $$2945\mathrm{.}16$ Mortgage Insurnce premium is $$2232$ Mortgage insurance premium rate is $3\mathrm{.}1\%.$Factor this into the overall cost.

C$.$ Analyze the impact of making additional annual payments of USD $$10,000$ towards the mortgage principal for each down payment option starting at the end of the $1$st year. How does this affect the total interest paid and the amortization period? Provide detailed calculation.

D$.$ Assume that funds not used for the down payment could be invested with an average annual return of $6\%.$ Calculate the potential value of these investments at the end of the mortgage period for each down payment option.

E$.$ Weigh the financial pros and cons of each down payment option.

F$.$ State and justify any assumptions made in your analysis, which may include economic factors, tax implications changes in the real estate market, or Xs financial situation.