To determine the maximum amount you can pay for a new home, we need to calculate the loan amount for which the monthly mortgage payment, excluding taxes and insurance, fits within your budget.

Here’s the step-by-step breakdown:

1. Determine the amount available for the down payment:

   • You have $10,723 available, but $2,000 is required for closing costs, so the down payment is: $\text{Down Payment} = 10,723 - 2,000 = 8,723$

2. Determine the monthly mortgage payment (P&I – Principal and Interest) you can afford:

   • Your total budget for housing expenses is $1,070.
   • From this, $150 goes toward taxes and insurance, leaving $920 for the mortgage payment (Principal and Interest): \text{Mortgage Payment (P&I)} = 1,070 - 150 = 920

3. Use the mortgage formula to determine the maximum loan amount: The monthly payment for a mortgage can be calculated using the formula for the present value of an annuity: $M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$ Where:

   • $M$ is the monthly mortgage payment ($920),
   • $P$ is the loan amount (which we are solving for),
   • $r$ is the monthly interest rate, which is the annual interest rate divided by 12 (6.5% annual interest rate gives $r = 0.065 / 12 = 0.005417$),
   • $n$ is the total number of monthly payments over 30 years (30 years = 360 months).

   Rearranging the formula to solve for $P$: $P = \frac{M \times \left( (1+r)^n - 1 \right)}{r \times (1+r)^n}$

4. Plug in the values: $P = \frac{920 \times \left( (1+0.005417)^{360} - 1 \right)}{0.005417 \times (1+0.005417)^{360}}$

   Calculating the factors: $(1+0.005417)^{360} \approx 6.68559$ Now substitute and solve: $P = \frac{920 \times (6.68559 - 1)}{0.005417 \times 6.68559}$ $P = \frac{920 \times 5.68559}{0.03621}$ $P \approx \frac{5,232.7428}{0.03621} \approx 144,469.22$

5. Add the down payment to find the maximum home price: Now, add the down payment of $8,723 to the loan amount: $\text{Maximum Home Price} = 144,469.22 + 8,723 = 153,192.22$

6. Compare with the given options: The closest option to this calculated value is $154,276.95.

Answer: $154,276.95

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Would you like more details on the calculations or another aspect of this process?

Here are 5 related questions to explore:

1. How does a higher interest rate affect the loan amount you can qualify for?
2. What would happen if your budget for the mortgage increased by $100 per month?
3. How do changes in down payment affect the total home price you can afford?
4. What if the term of the mortgage changed from 30 years to 15 years? How would that impact your payments?
5. How much could you afford with no closing costs, assuming the same budget?

Tip: Always check if there are programs or grants available for first-time homebuyers that could reduce your down payment or closing costs.