Carlos and Max are buying a house. They have $24000 for a down payment. The house price is $150000. If the interest rate is 8.85% compounded monthly, determine the size of the monthly payments they must make over the next 25 years to pay off the house.
Express your answer rounded to the nearest cent!
P = (Po*r*t)/(1-(1+r)^-t).
Po = 150,000-24,000 = $126,000.
r = 8.65%/(12*100%) = 0.0072.
t = 25yrs. * 12mo./yr. = 300 mo.
Monthly Payments = P/t.
To determine the size of the monthly payments, we can use the formula for the monthly payment on a mortgage.
The formula is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
M = monthly payment
P = principal or loan amount (house price minus down payment)
i = monthly interest rate (annual interest rate divided by 12 and expressed as a decimal)
n = total number of payments (12 payments per year multiplied by the number of years)
Let's calculate the values:
P = $150,000 - $24,000 = $126,000
i = 8.85% / 12 = 0.007375 (monthly interest rate)
n = 25 years * 12 = 300 (total number of payments)
Now, we can plug in these values into the formula:
M = $126,000 [ 0.007375(1 + 0.007375)^300 ] / [ (1 + 0.007375)^300 – 1 ]
Using a calculator, we can evaluate this expression to determine the size of the monthly payments. Rounding the answer to the nearest cent:
M ≈ $907.78
Therefore, Carlos and Max must make monthly payments of approximately $907.78 for the next 25 years to pay off the house.