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Question 4.P.4: A man plans to buy a $150 000 house. He wants to make a down......

A man plans to buy a $150 000 house. He wants to make a down payment of $30 000 and to take out a 30-year mortgage for the remaining $120 000, at 10% per year, compounded monthly. How much must he repay each month?

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Equation (2.6), with the appropriate substitutions, gives

A/P  =  \frac{i(1  +  i)^n}{(1  +  i)^n  –  1}  =  \frac{i}{1  –  (1  +  i)^{-n}}    (2.6) \\\\ A  =  \$120  000\frac{(0.10/12)(1  +  0.10/12)^{(12)(30)}}{(1  –  0.10/12)^{(12)(30)}  –  1}  =  \$120  000\frac{0.16531}{18.8374}  =  \$1053.08

The solution can also be approximated by use of (3.6):

\underset{n→∞}{\lim}(A/P,  i\%,  n)  =  i    (3.6)

A = $120 000(A/P, 10%, 360) ≈ $120 000(0.10/12) = $1000

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