Question

1. victor earns a gross annual income of $84,482 and is buying a home for $185,500. he is making a 15% down payment and financing the rest with a 25-year loan at 4.25% interest. monthly mortgage payment per $1000 borrowed rate 15-year loan 20-year loan 25-year loan 30-year loan 3.00% 6.906 5.546 4.742 4.216 3.25% 7.027 5.672 4.873 4.352 3.50% 7.149 5.800 5.006 4.490 3.75% 7.272 5.929 5.141 4.631 4.00% 7.397 6.060 5.278 4.774 4.25% 7.523 6.192 5.417 4.919 4.50% 7.650 6.326 5.558 5.067 4.75% 7.778 6.462 5.701 5.216 5.00% 7.908 6.600 5.846 5.368 (a) what is the mortgage amount he will borrow? (b) can he afford this mortgage? justify your response. (c) what will his monthly mortgage payment be? (d) what will his total payment for the house be? (e) what is the amount of interest he will pay? answer:

Explanation:

(a)

Step1: Calculate down payment

The down payment is 15% of the home price. So, down payment = \( 0.15 \times 185500 \)
\( 0.15 \times 185500 = 27825 \)

Step2: Calculate mortgage amount

Mortgage amount = Home price - Down payment = \( 185500 - 27825 \)
\( 185500 - 27825 = 157675 \)

Step1: Find monthly income

Annual income is \$84,482, so monthly income = \( \frac{84482}{12} \approx 7040.17 \)

Step2: Find monthly mortgage payment (from part c, we can use the value or calculate it here. Let's assume we use part c's result later, but for affordability, we can also check the debt-to-income ratio. Typically, a mortgage payment should be less than 28% of monthly income. First, let's find the monthly payment from part c: from part c, monthly payment is \$854.53 (wait, no, let's do it properly. Wait, in part c, we calculate the monthly payment. Wait, let's first do part c, but maybe for b, we can use the formula. Wait, the table is for monthly payment per \$1000 borrowed. So mortgage amount is \$157,675, which is LXI0 thousands. The rate is 4.25% for 25-year loan, so from the table, per \$1000, it's 5.417. So monthly payment = \( 157.675 \times 5.417 \approx 854.53 \). Now, monthly income is ~\$7040.17. 28% of monthly income is LXI2. Since \$854.53 < \$1971.25, he can afford it.

Step1: Determine per \$1000 payment

From the table, for 4.25% rate and 25-year loan, the monthly payment per \$1000 borrowed is 5.417.

Step2: Calculate mortgage amount in thousands

Mortgage amount is \$157,675, so in thousands, it's \( \frac{157675}{1000} = 157.675 \)

Step3: Calculate monthly payment

Monthly payment = \( 157.675 \times 5.417 \approx 157.675 \times 5.417 \approx 854.53 \) (wait, let's calculate 157.675 5.417: 157 5.417 = 1575 + 1570.417 = 785 + 65.469 = 850.469; 0.6755.417 ≈ 3.659; total ≈ 850.469 + 3.659 ≈ 854.13. Wait, maybe more accurate: 157675 / 1000 = 157.675. 157.675 5.417 = let's do 157.675 5 = 788.375, 157.675 0.417 = 157.675 0.4 + 157.675 0.017 = 63.07 + 2.680475 = 65.750475. Total = 788.375 + 65.750475 = 854.125475 ≈ \$854.13)

Answer:

\$157,675

(b)