Question

Mortgages, loans taken to purchase a property, involve regular payments at fixed intervals and are treated as reverse annuities. Mortgages are the reverse of annuities, because you get a lump-sum amount as a loan in the beginning, and then you make monthly payments to the lender. You’ve decided to buy a house that is valued at $1 million. You have $100,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $900,000 mortgage, and is offering a standard 30-year mortgage at a 12% fixed nominal interest rate (called the loan’s annual percentage rate or APR). Under this loan proposal, your mortgage payment will be per month. (Note: Round the final value of any interest rate used to four decimal places.)

Answer 1

Answer:

Ans. your monthly payment, for 30 years is $9,257.51 if you buy a property worth $1,000,000 and you make a down payment of $100,000

Explanation:

Hi, first we have to change the fixed rate in terms of an effective monthly rate, which is 1% effective monthly (12% nominal interest/12 =1% effective monthly). After that, take into account that the property is going to be paid in 30 years, but since the payments are going to be made in a montlhly basis, we have to turn years into months (30 years * 12 = 360 months).

After all that is done, all we have to do is to solve the following equiation for "A".

$PresentValue=\frac{A((1+r)^{n} -1)}{r(1+r)^{n} }$

Where:

A= Annuity or monthly payment

r= Rate (effective monthly, in our case)

n= Periods to pay (360 months)

Everything should look like this.

$900,000=\frac{A((1+0.01)^{360} -1}{0.01(1+0.0.1)^{360} }$

$900,000=A(97.2183311)$

$\frac{900,000}{97.2183311} =A$

$A=9,257.51$

Best of luck.