Mortgage lenders base the mortgage interest rate they offer you on your credit rating. This makes it financially critical to maintain a credit score of 700 or higher. How much more interest would you pay on a $195,000 home if you put 20% down and financed the remaining with a 30-year mortgage at 6% interest compared to a 30-year mortgage at 3 1/2 interest? Use 360 days a year.Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
195,000 * 0.8 = 156,000
I = PRT
I = 156,000 * 0.06 * 30
I = ?
I = 156,000 * 0.035 * 30
I = ?
280800
I'm not sure
To calculate the difference in interest paid on a $195,000 home with a 20% down payment and a 30-year mortgage at different interest rates, we need to follow these steps:
Step 1: Calculate the loan amount.
Since you're putting a 20% down payment, you'll be financing 80% of $195,000, which is $156,000.
Step 2: Calculate the monthly interest rate.
To convert the annual interest rate to a monthly rate, divide the annual rate by 12. For the first scenario with a 6% interest, the monthly interest rate would be 6% / 12 = 0.5%.
Step 3: Calculate the number of months.
In a 30-year mortgage, you'll make payments for 30 years, which is equal to 30 * 12 = 360 months.
Step 4: Calculate the monthly payment.
To calculate the monthly payment amount, we can use the loan amount, monthly interest rate, and the number of months. We can use the following formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
M = monthly payment
P = loan amount
i = monthly interest rate
n = number of months
For the first scenario with a 6% interest rate:
i = 0.5% (0.005 in decimal form)
n = 360
P = $156,000
Plug in the values into the formula:
M = 156000 [ 0.005(1 + 0.005)^360 ] / [ (1 + 0.005)^360 – 1 ]
Using a financial calculator or spreadsheet software, the calculated monthly payment would be $935.23.
Step 5: Calculate the total interest paid.
To find the total interest paid over the course of 30 years, multiply the monthly payment by the number of months and subtract the loan amount. Then round your answer to the nearest dollar amount.
Total Interest Paid = (M * n) - P
Total Interest Paid = (935.23 * 360) - 156000
Total Interest Paid = $336,283.15 - $156,000
Total Interest Paid = $180,283.15
For the second scenario with a 3 1/2 % interest rate, repeat the steps above using an interest rate of 3.5% instead of 6%.
Using the same process:
P = $156,000
i = 3.5% / 12 = 0.2917% (0.002917 in decimal form)
n = 360
Using the formula, we find the monthly payment to be $699.21.
Total Interest Paid = (M * n) - P
Total Interest Paid = (699.21 * 360) - 156000
Total Interest Paid = $251,716.88 - $156,000
Total Interest Paid = $95,716.88
Therefore, the difference in interest paid on a $195,000 home with a 20% down payment between a 30-year mortgage at 6% interest and a 30-year mortgage at 3 1/2% interest is $180,283.15 - $95,716.88 = $84,566.27.