Question 1186435
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Tina is buying a new apartment. She can afford a mortgage payment of $1050 a month, 
and a down payment of $16000. She obtained a 18 year loan at 8% compounded monthly. 
What is the most expensive apartment she can buy?
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<pre>
Use the formula for the monthly payment for a mortgage

    M = {{{L*(r/(1-(1+r)^(-n)))}}}


where L is the loan amount; r = {{{0.08/12}}} is the effective interest rate per month;
n is the number of payments (same as the number of months); M is the monthly payment.


From this formula, the expression for the maximum loan is

    L = {{{M/((r/(1-(1+r)^(-n))))}}}.


In this problem  M = $1050;  r = {{{0.08/12}}},  n = 18*12 = 216 monthly payments.


Substitute these values into the formula and get for the maximum mortgage amount

    L = {{{1050/(((0.08/12)/(1-(1+0.08/12)^(-216))))}}} = $120,005.13  (rounded).


Thus, the maximum mortgage amount is about $120,000.

Add to it the down payment of $16,000  to get the most expensive price for the apartment 
of $120,000 + $16,000 = $136,000.    <U>ANSWER</U>
</pre>

Solved.