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Sagot :
Let's solve this problem by breaking it into two parts: calculating the total rental cost and the total buying cost.
### Part a: Calculate total rental cost and total buying cost
#### Total Rental Cost Calculation
1. Annual Rent: \$7,560
2. Insurance Rent: \$245
3. Security Deposit: \$630
To find the total rental cost, we sum these costs:
[tex]\[ \text{Total Rental Cost} = \text{Annual Rent} + \text{Insurance Rent} + \text{Security Deposit} \][/tex]
Substituting in the actual numbers:
[tex]\[ \text{Total Rental Cost} = 7,560 + 245 + 630 = 8,435 \][/tex]
So, the total rental cost is \$8,435.
#### Total Buying Cost Calculation
1. Annual Mortgage Payments: \$18,880
2. Property Taxes: \$2,180
3. Down Payment and Closing Costs: \$5,500
4. Insurance and Maintenance: \$1,218
5. Growth in Equity: \$5,375 (this is a benefit, so it will be subtracted)
6. Estimated Annual Appreciation: \$2,600 (this is also a benefit, so it will be subtracted)
To find the total buying cost, we use the following formula:
[tex]\[ \text{Total Buying Cost} = \text{Annual Mortgage Payments} + \text{Property Taxes} + \text{Insurance and Maintenance} + \text{Down Payment and Closing Costs} - \text{Growth in Equity} - \text{Estimated Annual Appreciation} \][/tex]
Substituting in the actual numbers:
[tex]\[ \text{Total Buying Cost} = 18,880 + 2,180 + 1,218 + 5,500 - 5,375 - 2,600 = 19,803 \][/tex]
So, the total buying cost is \$19,803.
### Part b: Would you recommend buying or renting?
Based on the calculated costs:
- Total Rental Cost: \$8,435
- Total Buying Cost: \$19,803
Since the total rental cost (\[tex]$8,435) is significantly lower than the total buying cost (\$[/tex]19,803), it would be more financially advantageous to rent rather than buy in this scenario.
Conclusion in tabular form:
[tex]\[ \begin{array}{|c|c|} \hline \text{a. Rental Cost} & \$8,435 \\ \hline \text{a. Buying Cost} & \$19,803 \\ \hline \text{b. Would you recommend buying or renting?} & \text{Renting} \\ \hline \end{array} \][/tex]
### Part a: Calculate total rental cost and total buying cost
#### Total Rental Cost Calculation
1. Annual Rent: \$7,560
2. Insurance Rent: \$245
3. Security Deposit: \$630
To find the total rental cost, we sum these costs:
[tex]\[ \text{Total Rental Cost} = \text{Annual Rent} + \text{Insurance Rent} + \text{Security Deposit} \][/tex]
Substituting in the actual numbers:
[tex]\[ \text{Total Rental Cost} = 7,560 + 245 + 630 = 8,435 \][/tex]
So, the total rental cost is \$8,435.
#### Total Buying Cost Calculation
1. Annual Mortgage Payments: \$18,880
2. Property Taxes: \$2,180
3. Down Payment and Closing Costs: \$5,500
4. Insurance and Maintenance: \$1,218
5. Growth in Equity: \$5,375 (this is a benefit, so it will be subtracted)
6. Estimated Annual Appreciation: \$2,600 (this is also a benefit, so it will be subtracted)
To find the total buying cost, we use the following formula:
[tex]\[ \text{Total Buying Cost} = \text{Annual Mortgage Payments} + \text{Property Taxes} + \text{Insurance and Maintenance} + \text{Down Payment and Closing Costs} - \text{Growth in Equity} - \text{Estimated Annual Appreciation} \][/tex]
Substituting in the actual numbers:
[tex]\[ \text{Total Buying Cost} = 18,880 + 2,180 + 1,218 + 5,500 - 5,375 - 2,600 = 19,803 \][/tex]
So, the total buying cost is \$19,803.
### Part b: Would you recommend buying or renting?
Based on the calculated costs:
- Total Rental Cost: \$8,435
- Total Buying Cost: \$19,803
Since the total rental cost (\[tex]$8,435) is significantly lower than the total buying cost (\$[/tex]19,803), it would be more financially advantageous to rent rather than buy in this scenario.
Conclusion in tabular form:
[tex]\[ \begin{array}{|c|c|} \hline \text{a. Rental Cost} & \$8,435 \\ \hline \text{a. Buying Cost} & \$19,803 \\ \hline \text{b. Would you recommend buying or renting?} & \text{Renting} \\ \hline \end{array} \][/tex]
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