RESIDENTIAL MORTGAGE FINANCING:

Question $1$:

You are considering buying a $$400,000$ house. Bank offers a $90$ percent LTV $($loan to value$),$ a $30$ year mortgage, a fixed annual rate of $6$ percent, and monthly payments. Calculate the monthly payment.

Question $2$:

i$)$ Find the remaining mortgage balance at the end of $15$ years for a $30-$year loan, worth $$550,000,5$ percent annual interest, and monthly payments.

ii$)$ How much total principal has the borrower paid for the $15$ years?

iii$)$ How much total interests has the borrower paid for the $15$ years?

Question $3$:

Consider a $25-$year loan with an annual interest rate of $7$ percent and monthly payments of $$1,201\mathrm{.}52($to be precise$).$ The discount points charged by the lender at origination are $3$ percent. Additional fees paid to other third parties $($i$.$e$.,$ not the lender$)$ is $$4,000.$

Required:

a$.$ Calculate the loan amount?

b$.$ What is the lender's yield$/$IRR$?$

c$.$ What is the effective borrowing cost $($EBC$)?$