shawn bought a home for $100,000. he put 20% down and obtained a mortguage for 30 years at 5 1/2%. what is the total cost of the loan? can you show me how this is worked out?
To find the total cost of the loan, we need to calculate the sum of the down payment and the interest paid over the 30-year mortgage term.
Step 1: Calculate the down payment
The down payment is 20% of the home's price, which is $100,000. To find the down payment, multiply the price by the percentage: $100,000 x 0.2 = $20,000.
Step 2: Calculate the loan amount
The loan amount is the remaining balance after the down payment. Subtract the down payment from the home price: $100,000 - $20,000 = $80,000. Therefore, the loan amount is $80,000.
Step 3: Calculate monthly mortgage payment
Use the loan amount and interest rate to determine the monthly mortgage payment. First, convert the interest rate from a mixed fraction to a decimal: 5 1/2% = 5.5% = 5.5/100 = 0.055.
Next, use the loan amount, interest rate, and mortgage term to calculate the monthly payment using the following formula:
P = (r * A) / (1 - (1 + r)^(-n))
where:
P = monthly payment
A = loan amount
r = monthly interest rate (annual interest rate divided by 12)
n = total number of payments (number of years multiplied by 12, assuming monthly payments)
P = (0.055 * $80,000) / (1 - (1 + 0.055)^(-30*12))
Calculating this equation gives us a monthly payment of $453.28.
Step 4: Calculate total interest paid over the 30-year loan term
Multiply the monthly mortgage payment by the total number of payments (30 years * 12 months per year) to find the total payments made over the life of the loan: $453.28 * 30 * 12 = $163,204.80.
Subtract the original loan amount from the total of all payments to determine the total interest paid: $163,204.80 (total payments) - $80,000 (loan amount) = $83,204.80.
Finally, the total cost of the loan, including the down payment and the interest paid, is the sum of the down payment and the total interest paid: $20,000 (down payment) + $83,204.80 (total interest) = $103,204.80.
Therefore, the total cost of the loan is $103,204.80.