To determine whether it's better to buy or rent, we will compare the total cost of renting to the total cost of buying, incorporating various factors such as tax deductions, interest savings, and appreciation.

Step 1: Calculate the total rental cost.

• Annual rent: $7,730
• Insurance: $180
• Security deposit: $825 (only paid once upfront, so we'll exclude it for annual cost comparisons)

So, the annual total rental cost is: $\text{Rental cost} = 7,730 + 180 = 7,910$

Step 2: Calculate the total buying cost.

a. Mortgage interest deduction and tax savings:

• Annual mortgage interest: $9,750
• Tax rate: 26%

The mortgage interest is deductible, so the tax savings from this deduction is: $\text{Tax savings} = 9,750 \times 0.26 = 2,535$

b. After-tax cost of mortgage interest:

$\text{After-tax mortgage interest} = 9,750 - 2,535 = 7,215$

c. Property taxes:

• Property taxes: $1,920

Property taxes are not deductible because of the assumption about other deductions exceeding the standard deduction.

d. Insurance and maintenance:

• Insurance and maintenance: $1,400

e. Annual appreciation:

• Annual appreciation: $2,050

This appreciation reduces the effective cost of buying.

f. Growth in equity:

• Growth in equity: $750

This represents an increase in the homeowner's wealth and reduces the effective cost of buying.

g. Opportunity cost of the down payment:

The down payment is $5,200. If this money were instead saved at an after-tax interest rate of 5%, the opportunity cost of not having this money invested is: $\text{Opportunity cost} = 5,200 \times 0.05 = 260$

Step 3: Total cost of buying:

Now, let's sum up all relevant costs:

$\text{Total cost of buying} = (\text{After-tax mortgage interest}) + (\text{Property taxes}) + (\text{Insurance and maintenance}) - (\text{Appreciation}) - (\text{Growth in equity}) + (\text{Opportunity cost of down payment})$

Substitute the values:

$\text{Total cost of buying} = 7,215 + 1,920 + 1,400 - 2,050 - 750 + 260 = 7,995$

Step 4: Compare the costs

• Total rental cost: $7,910
• Total buying cost: $7,995

The total annual cost of buying ($7,995) is slightly higher than the cost of renting ($7,910) by $85.

Recommendation:

The difference is minimal, but since the costs are so close, buying may be a better option in the long term due to potential future appreciation in property value and equity growth, even though renting is marginally cheaper in the short term. The decision to buy also comes with the potential for future returns on investment through home appreciation, which renting does not provide.

Would you like any further details or clarification on this?

Here are 5 related questions for further exploration:

1. How would changing the appreciation rate affect the decision between buying and renting?
2. What if the mortgage interest rate were higher? How would that change the recommendation?
3. How would inflation impact future costs for both renting and buying?
4. What would happen if property taxes or insurance rates increased significantly?
5. How does the length of time planning to stay in the home affect the buy vs. rent decision?

Tip: Always consider how long you plan to stay in a property when deciding between renting and buying; the longer you stay, the more advantageous buying becomes due to equity and appreciation.