Shawn bought a home for $100,000. He put 20% down and obtained a mortgage for 30
years at 5½%. What is the total interest cost of the loan?
waqs it $158,400.00? but i still need to see how to work the problem, can you be of help to me?
M = P [ i(1 + i)n ] / [ (1 + i)n - 1]
M is the monthly payment; i = rate/12; n=number of payments
For an $80,000 mortgage at 5.5% compounded monthly for 30 years, we would first solve for i as
i = 0.055 / 12 = 0.0045833333 and n as 12 x 30 = 360 monthly payments
i = 0.05 / 12 = 0.004167 and n as 12 x 15 = 180 monthly payments
Next solve for (1 + i)n = (1.0045833333)360 using the xy key on a calculator, which yields 5.187388
Now the formula reads M = P [ i(5.187388)] / [5.187388 - 1] which simplifies to
M = P [0.0045833333 x 5.187388] / 4.187388 or
M = $80,000 x 0.005678899 = $454.23
To determine the total interest paid over the course of the mortgage, multiply the amount of the monthly payment by the number of payments and subtract the principal:
($454.23 x 360) - $80,000 = $163,522.80 - $80,000 = $83,522.80 total interest
no my given answers are (a) $158,400.00 (b) $104,480.00 (c) $83,584.00 (d) $63,584.00 now which one is the given ics answer?
To calculate the total interest cost of the loan, we first need to calculate the loan amount, which is the total cost of the home minus the down payment.
Given that Shawn put 20% down on a $100,000 home, the down payment can be calculated as follows:
Down payment = 20% × $100,000 = $20,000
Now, to find the loan amount, we subtract the down payment from the total cost of the home:
Loan amount = Total cost of the home - Down payment = $100,000 - $20,000 = $80,000
Next, we need to calculate the annual interest rate, which is given as 5½%. However, to use it in our calculations, we need to convert it to a decimal. We divide 5½% by 100 to get the decimal equivalent:
Annual interest rate = 5½% ÷ 100 = 0.055
Since the mortgage is for 30 years, we also need to calculate the total number of monthly payments. We multiply the number of years by 12 to get the total number of months:
Total number of monthly payments = 30 years × 12 months/year = 360 months
To calculate the monthly interest rate, we divide the annual interest rate by 12:
Monthly interest rate = Annual interest rate ÷ 12 = 0.055 ÷ 12 = 0.00458
Now, we can calculate the monthly payment using the loan amount, monthly interest rate, and the total number of monthly payments. We'll use the formula for calculating the fixed monthly payment on a mortgage:
Monthly payment = [Loan amount × Monthly interest rate] / [1 - (1 + Monthly interest rate)^(-Total number of monthly payments)]
Finally, to find the total interest cost of the loan, we multiply the monthly payment by the total number of monthly payments, and then subtract the loan amount:
Total interest cost = (Monthly payment × Total number of monthly payments) - Loan amount
By plugging in the values and calculating the equation, we can find the total interest cost.