Questions: You can afford monthly payments of 800. If current mortgage rates are 2.08% for a 15-year fixed rate loan, how much can you afford to borrow? If you are required to make a 10% down payment and you have the cash on hand to do it, how expensive a home can you afford? (Hint: You will need to solve the loan payment formula for P.) How much can you afford to borrow? (Round to the nearest dollar as needed.)

You can afford monthly payments of 800. If current mortgage rates are 2.08% for a 15-year fixed rate loan, how much can you afford to borrow? If you are required to make a 10% down payment and you have the cash on hand to do it, how expensive a home can you afford? (Hint: You will need to solve the loan payment formula for P.)

How much can you afford to borrow?
(Round to the nearest dollar as needed.)

Transcript text: You can afford monthly payments of $\$ 800$. If current mortgage rates are $2.08 \%$ for a 15 -year fixed rate loan, how much can you afford to borrow? If you are required to make a $10 \%$ down payment and you have the cash on hand to do it, how expensive a home can you afford? (Hint: You will need to solve the loan payment formula for P.) How much can you afford to borrow? \$ (Round to the nearest dollar as needed.)

Solution

Solution Steps

Step 1: Convert the annual interest rate to a monthly interest rate

To convert the annual interest rate of 2.08% to a monthly interest rate, we divide it by 12 and then convert it to a decimal by dividing by 100. Thus, the monthly interest rate, $i$, is 0.00173.

Step 2: Calculate the total number of payments

The total number of payments over the term of the loan, given the term is 15 years, is $n \times 12 = 180$ payments.

Step 3: Calculate the loan amount you can afford to borrow

Using the formula $P = M \times \frac{1 - (1 + i)^{-t}}{i}$, where $M$ is the monthly payment you can afford, $i$ is the monthly interest rate, and $t$ is the total number of payments, we find that the loan amount $P$ you can afford is $123610.

Step 4: Calculate the maximum price of the home you can afford

Considering the required down payment percentage of 10%, the maximum price of the home you can afford is calculated as $\frac{P}{1 - d}$, which equals $137344.