Consider a $15-$year, fixed$-$rate mortgage for $$240,000$ at an annual rate of $5\mathrm{.}2\%.$ How much of the total expenses on mortgage payments go toward principal and interest during a$)$ the first month, b$)$ the second month, c$)$ the first year, d$)$ the second year, e$)$ the third year, $f)$ the first two years, $g)$ the first three years?

The purchase a house costing $$1,000,000,$ a loan for $70$ percent of the acquisition price is taken. The loan has an interest rate of $8$ percent, $30-$year term and fixed monthly payment.

a$)$ Calculate the monthly mortgage payment. What is the total expense per year?

b$)$ Calculate the loan balance at the end of years $1,2,3,$ and $4.$

c$)$ Calculate the amount of principal reduction ashieved during each of the first four years.

d$)$ Calculate the total interest paid during each of the first four years.

Consider a $5-$year balloon loan for $$100,000.$ The bank requires a monthly payment equal to that of a $30-$year fixed$-$rate loan with a nominal annual rate of $5\mathrm{.}5\%.$ How much will the borrower owe when the balloon payment is due? Construct the loan amortization schedule.

Consider a $30-$year, fixed$-$rate mortgage for $$500,000$ at a nominal rate of $6\%.$ What is the difference in required payments between a monthly payment and a bi$-$monthly payment $($payments