shawn bought a home for $100000.he put 20% down and obtained a mortgage for 30 years at 51/2%.what is the total interest cost of the loan? i need the steps worked.
% Loan = 100% - 20% = 80%.
Amt of Loan = 0.8 * $100,000 = $80,000.
Pt = Po*r*t / (1-(1+r)^-t),
r = (5.5% / 12) / 100$ = 0.00458 = monthly % rate expressed as a decimal.
t = 30yrs * 12mo/yr = 360mo.
Pt=80000*0.004583333*360/(1-(1.004583333)^-360 = $163,523.23.
Int. = 163,523.23 - 80,000 = $83,523.23
well, the answer came out in ics as $104,480.00 but as i figured it 100,000/1000=100x5.68 so 5.68x360=204,480.00-100000.00=$104,480.00 that was i got but see is the 20% figured in that figure?
$63,584.00is the correct answer.
$80 x 5.68 = 454.40
454.40 x 360 = 163,584.00
163,584.00 - 100,000 = $63,584.00
D.) $63,584.00
To find the total interest cost of the loan, we need to calculate the amount of the mortgage and the monthly payment. Then, we can subtract the original loan amount from the total amount paid over the 30-year period. Here are the steps:
Step 1: Calculate the amount of the mortgage:
Since Shawn put a 20% down payment, the remaining amount of the mortgage can be calculated as:
Mortgage amount = Purchase price - Down payment
Mortgage amount = $100,000 - ($100,000 * 0.2)
Mortgage amount = $100,000 - $20,000
Mortgage amount = $80,000
Step 2: Calculate the monthly interest rate:
The annual interest rate is 5.5%, so we need to convert it into a monthly rate. Divide the annual interest rate by 12 to get the monthly rate:
Monthly interest rate = 5.5% / 100 / 12
Monthly interest rate = 0.055 / 12
Monthly interest rate = 0.0045833 (rounded to 6 decimal places)
Step 3: Calculate the number of monthly payments:
Since the loan term is 30 years, multiply the number of years by 12 to get the number of monthly payments:
Number of monthly payments = 30 years * 12
Number of monthly payments = 360
Step 4: Calculate the monthly payment using the mortgage formula:
To calculate the monthly payment, we can use the mortgage formula:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of monthly payments))
For our calculations:
Loan amount = $80,000
Monthly interest rate = 0.0045833
Number of monthly payments = 360
Plug these values into the formula and calculate the monthly payment.
Step 5: Calculate the total amount paid over the 30-year period:
Total amount paid = Monthly payment * Number of monthly payments
Step 6: Calculate the total interest cost:
Total interest cost = Total amount paid - Mortgage amount
Now, let's calculate:
Step 1:
Mortgage amount = $80,000
Step 2:
Monthly interest rate = 0.0045833
Step 3:
Number of monthly payments = 360
Step 4:
Using the mortgage formula, Monthly payment = ($80,000 * 0.0045833) / (1 - (1 + 0.0045833)^(-360))
Monthly payment ≈ $453.84 (rounded to the nearest cent)
Step 5:
Total amount paid = $453.84 * 360
Total amount paid = $163,382.40
Step 6:
Total interest cost = $163,382.40 - $80,000
Total interest cost = $83,382.40
Therefore, the total interest cost of the loan is approximately $83,382.40.