Question

You bought a house worth ​$. you paid​ 25% of the purchase price in cash and arranged a ​-year mortgage with a rate of ​% compounded​ semi-annually for the remaining balance. the mortgage has an amortization period of years. after having made payments for years​ (starting at the end of the first​ month), what will the outstanding balance of the mortgage​ be?

Answer 1

To find the outstanding balance of the mortgage after making payments for a certain number of years, use the present value formula and the formula for the outstanding balance. Calculate the annual mortgage payment using the present value formula and then use it to find the outstanding balance after a certain number of years of payments.

Step-by-step explanation:

To find the outstanding balance of the mortgage after making payments for a certain number of years, we need to use the formula for the present value of an annuity. In this case, the annuity is the mortgage payment made each year, the interest rate is the rate of the mortgage compounded semi-annually, and the number of periods is the amortization period.

Using the given information, we can calculate the annual mortgage payment using the present value formula:

Loan Amount = P * (1 - (1 + r/n)^(-nt))/(r/n)

where P is the principal loan amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Once we know the annual mortgage payment, we can use it to calculate the outstanding balance of the mortgage after a certain number of years using the formula:

Outstanding Balance = Loan Amount * (1 - (1 + r/n)^(-n(t-y)))/(r/n)

where y is the number of years of payments made.