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Question 1206647: Suppose you can afford to pay at most $1000 per month for a mortgage payment. If the maximum amortization period you can get is 20 years, and you must pay 7.5% interest per year compounded monthly, what is the most expensive house you can buy? How much interest will you have paid to the lender at the end of the loan?
What is the monthly interest rate corresponding to the effective annual rate?
What is the price of the most expensive house you can buy?
What is the total interest paid?
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Suppose you can afford to pay at most $1000 per month for a mortgage payment.
If the maximum amortization period you can get is 20 years,
and you must pay 7.5% interest per year compounded monthly,
(a) what is the most expensive house you can buy?
(b) How much interest will you have paid to the lender at the end of the loan?
(c) What is the monthly  interest rate corresponding to the   annual rate?
(d) What is the price of the most expensive house you can buy?
(e) What is the total interest paid?
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In your post, the terms in question (c) were named incorrectly;
so, I edited it to make them correct.
Pay attention to it and learn terminology.
It is important to know precise terminology and to use it correctly.
It determines your level as a Math writer.
Use the formula for the monthly payment for a mortgage
M = 
where P is the loan amount; r =  is the effective interest rate per month;
n is the number of payments (same as the number of months in this problem);
M is the monthly payment.
From this formula, the expression for the maximum loan is
P =  .
In this problem M = $1000; r = , n = 20*12 = 240 monthly payments.
Substitute these values into the formula and get for the maximum loan amount
P =  = $124,132.14.
Thus, the maximum mortgage amount is $124,132, which means that
the most expensive house is about $124,132. ANSWER to questions (a) and (d)
The total interest you pay to the lender is
20*12*1000 - 124,132 = 240000 = 115,868 dollars. ANSWER to question (e)
The answer to question (c) is r = 0.075/12 = 0.00625.
Solved.
I leave without answer your question (b), since there are just too many questions in this post.
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