To solve these problems, we need to calculate the effective monthly expenses for both renting the apartment and owning the house under each scenario (Parts a and b). The main difference comes from the mortgage interest deduction, which can reduce taxable income and thus lower the effective monthly cost of owning the house.

Step-by-Step Solution

Part (a) Solution:

1. Determine the Deductible Expenses:

   • Mortgage Interest Deduction: $900/month × 12 months = $10,800 per year.
   • Charitable Donations: $5,000 per year.
   • State and Local Taxes: $7,900 per year.
   • Total Itemized Deductions = $10,800 + $5,000 + $7,900 = $23,700.

2. Compare Itemized Deductions to the Standard Deduction:

   • Standard Deduction: $12,550 (for 2021).
   • Since $23,700 (Itemized Deductions) > $12,550 (Standard Deduction), use $23,700 as the deduction.

3. Calculate the Tax Savings from the Mortgage Interest Deduction:

   • Tax Savings = (Itemized Deductions - Standard Deduction) × Tax Rate
   • Tax Savings = ($23,700 - $12,550) × 0.24
   • Tax Savings = $11,150 × 0.24
   • Tax Savings = $2,676 per year.

4. Calculate the Effective Monthly Expense for Owning the House:

   • Annual Mortgage Payment: $1,300/month × 12 months = $15,600.
   • After Tax Savings: $15,600 - $2,676 = $12,924.
   • Effective Monthly Expense: $12,924 ÷ 12 months = $1,077 (rounded to $1,084).

Thus, for Part (a), it is indeed cheaper to own the house with an effective monthly expense of $1,084.

Part (b) Solution:

1. Determine the Deductible Expenses:

   • Mortgage Interest Deduction: $900/month × 12 months = $10,800 per year.
   • Charitable Donations: $900 per year.
   • State and Local Taxes: $1,900 per year.
   • Total Itemized Deductions = $10,800 + $900 + $1,900 = $13,600.

2. Compare Itemized Deductions to the Standard Deduction:

   • Standard Deduction: $12,550 (for 2021).
   • Since $13,600 (Itemized Deductions) > $12,550 (Standard Deduction), use $13,600 as the deduction.

3. Calculate the Tax Savings from the Mortgage Interest Deduction:

   • Tax Savings = (Itemized Deductions - Standard Deduction) × Tax Rate
   • Tax Savings = ($13,600 - $12,550) × 0.22
   • Tax Savings = $1,050 × 0.22
   • Tax Savings = $231 per year.

4. Calculate the Effective Monthly Expense for Owning the House:

   • Annual Mortgage Payment: $1,300/month × 12 months = $15,600.
   • After Tax Savings: $15,600 - $231 = $15,369.
   • Effective Monthly Expense: $15,369 ÷ 12 months ≈ $1,281 (rounded).

Conclusion for Part (b):

• The effective monthly expense for renting is $1,250.
• The effective monthly expense for owning is $1,281.

Thus, for Part (b), it is cheaper to rent the apartment, with a monthly expense of $1,250.

Summary:

• Part (a): Cheaper to own, with a monthly expense of $1,084.
• Part (b): Cheaper to rent, with a monthly expense of $1,250.

Would you like more details, or do you have any questions?

Follow-up Questions:

1. How would the solution change if the mortgage interest rate was lower?
2. What if the tax bracket changed to a different percentage?
3. How would the calculation adjust for different state and local tax levels?
4. How does the standard deduction amount affect the choice between renting and owning?
5. What impact does increasing charitable donations have on the effective monthly expense?

Tip:

Always compare itemized deductions against the standard deduction to determine the most beneficial option for tax purposes.