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.)

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".

Where:

A= Annuity or monthly payment

r= Rate (effective monthly, in our case)

n= Periods to pay (360 months)

Everything should look like this.

Best of luck.

two years ago, when picking flowers in the mountains back of yosemite valley, i found a book. it was blotted and storm-beaten; all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however; many of the inner pages were well preserved. and although all were more or less stained and torn, whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today; its granite pages have been torn and blurred by the same storms that wasted the castaway book.

two years ago, when picking flowers in the mountains back of yosemite valley; i found a book. it was blotted and storm-beaten, all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however, many of the inner pages were well preserved. and although all were more or less stained and torn; whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today, its granite pages have been torn and blurred by the same storms that wasted the castaway book.