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Math  /  Data & Statistics

Question2. Estimate the affordable monthly mortgage payment, the affordable mortgage amount, and the affordable home purchase price for the following situation (Figure 9.1.4 Mortgage Affordability Calculation).
Monthly gross income, \$4,167 Down payment to be made-15 percent of purchase price
Other debt (monthly payment), \$500 Monthly Property Taxes and Home Insurance, \$200 30-year loan at 8 percent a. Affordable monthly mortgage payment b. Affordable mortgage amount c. Affordable home purchase

Studdy Solution

STEP 1

1. The monthly gross income is \$4,167.
2. The down payment is 15% of the purchase price.
3. Other monthly debt payments are \$500.
4. Monthly property taxes and home insurance total \$200.
5. The loan term is 30 years with an 8% annual interest rate.
6. The calculation follows standard mortgage affordability guidelines.

STEP 2

1. Calculate the affordable monthly mortgage payment.
2. Calculate the affordable mortgage amount.
3. Calculate the affordable home purchase price.

STEP 3

Calculate the maximum allowable monthly housing expense using the 28/36 rule, which states that housing expenses should not exceed 28% of gross income, and total debt should not exceed 36% of gross income.
Maximum housing expense=0.28×4,167=1,166.76 \text{Maximum housing expense} = 0.28 \times 4,167 = 1,166.76
Maximum total debt expense=0.36×4,167=1,500.12 \text{Maximum total debt expense} = 0.36 \times 4,167 = 1,500.12

STEP 4

Subtract the other debt payments and property taxes/insurance from the maximum total debt expense to find the affordable monthly mortgage payment.
Affordable monthly mortgage payment=1,500.12−500−200=800.12 \text{Affordable monthly mortgage payment} = 1,500.12 - 500 - 200 = 800.12

STEP 5

Calculate the affordable mortgage amount using the monthly mortgage payment, the interest rate, and the loan term. Use the formula for the monthly payment of an amortizing loan:
M=Pr(1+r)n(1+r)n−1 M = P \frac{r(1+r)^n}{(1+r)^n-1}
Where: - M M is the monthly mortgage payment (\$800.12), - \( r \) is the monthly interest rate (8% annual = 0.08/12 per month), - \( n \) is the total number of payments (30 years \(\times\) 12 months/year = 360), - \( P \) is the loan principal (affordable mortgage amount).
Rearrange to solve for P P :
P=M×((1+r)n−1)r(1+r)n P = \frac{M \times ((1+r)^n-1)}{r(1+r)^n}
P=800.12×((1+0.08/12)360−1)(0.08/12)(1+0.08/12)360 P = \frac{800.12 \times ((1+0.08/12)^{360}-1)}{(0.08/12)(1+0.08/12)^{360}}
Calculate P P .

STEP 6

Calculate the affordable home purchase price by adding the down payment to the affordable mortgage amount. The down payment is 15% of the purchase price.
Let x x be the purchase price, then:
0.85x=P 0.85x = P
x=P0.85 x = \frac{P}{0.85}
Calculate x x .
The affordable monthly mortgage payment is approximately \$800.12, the affordable mortgage amount is calculated from the formula above, and the affordable home purchase price is derived from the mortgage amount and down payment percentage.

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