The monthly payment for a home mortgage or car loan is computed by the formula
M = Pr
_____
1 – (1 + R)^-n
Where P is the initial amount borrowed, r is the monthly interest rate (This is the annual rate divided by 12), and n is the number of monthly payments (This is the number of years of loan times 12). Suppose that the annual rate of a particular 30 year mortgage is 8%.
(a) Compare the monthly payment for a mortgage of 100,000 $. what is the total amount paid over 30 years
(b) How much could be borrowed initially if the monthly payment cannot exceed $1000.
M = 100000(0.08/12) / (1 – (1+0.08/12)^-360) = $733.76 is the monthly payment. Over 30 years (360 months) the total paid will be 733.76(360) = $264155.
The monthly payment is proportional to the amount borrowed so x / 100000 = 1000 / 733.76 is an equation to find the maximum mortgage loan to keep the payment below $1000 if the interest rate is 8%.
x = $136,300 is the maximum mortgage amount to keep the payment below $1000 monthly.
M = 100000(0.08/12) / (1 – (1+0.08/12)^-360) = $733.76 is the monthly payment. Over 30 years (360 months) the total paid will be 733.76(360) = $264155.
The monthly payment is proportional to the amount borrowed so x / 100000 = 1000 / 733.76 is an equation to find the maximum mortgage loan to keep the payment below $1000 if the interest rate is 8%.
x = $136,300 is the maximum mortgage amount to keep the payment below $1000 monthly.
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