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 740 or higher. How much more interest would you pay on a $\$ 199,000$ home if you put $25 \%$ down and financed the remaining with a 30 -year mortgage at $5 \%$ interest compared to a 30 -year mortgage at $3.5 \%$ interest? (Do not round intermediate calculations. Round your answer to the nearest cent.)

Excess interest

Step 1 ：First, calculate the amount that is financed by subtracting the down payment from the total cost of the home. The down payment is 25% of the total cost of the home, which is $199,000. So, the financed amount is $199,000 - 0.25*$199,000 = $149,250.

Step 2 ：Next, calculate the total interest paid over the course of the 30-year mortgage for both interest rates. The formula for the total interest paid on a mortgage is: \(\text{Interest} = P*r*(1 - (1 + r)^{-n})/r\), where P is the principal amount (the loan amount), r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (years times 12).

Step 3 ：For the higher interest rate of 5%, the monthly interest rate is 0.05/12 = 0.004167. So, the total interest paid is $149,250*0.004167*(1 - (1 + 0.004167)^{-360})/0.004167 = $115,843.88.

Step 4 ：For the lower interest rate of 3.5%, the monthly interest rate is 0.035/12 = 0.002917. So, the total interest paid is $149,250*0.002917*(1 - (1 + 0.002917)^{-360})/0.002917 = $96,941.91.

Step 5 ：Finally, subtract the total interest paid at the lower interest rate from the total interest paid at the higher interest rate to find the excess interest. So, the excess interest is $115,843.88 - $96,941.91 = $18,901.97.

Step 6 ：\(\boxed{\text{Final Answer: The excess interest you would pay on a $199,000 home if you put 25% down and financed the remaining with a 30-year mortgage at 5% interest compared to a 30-year mortgage at 3.5% interest is approximately $18,901.97.}}\)