Answer :
### Step-by-Step Solution:
1. Identify the given information:
- Mortgage amount (Principal): \[tex]$300,000 - Monthly payment: \$[/tex]1,000
- Total interest paid over the loan duration: \[tex]$60,000 - Duration of the loan: 30 years 2. Calculate the total number of payments: \[\text{Number of years} \times 12 = 30 \text{ years} \times 12 = 360 \text{ payments}\] 3. Calculate the total repayment amount: \[\text{Monthly payment} \times \text{Number of payments} = \$[/tex]1,000 \times 360 = \[tex]$360,000\] 4. Calculate the amount paid towards the principal: This is essentially the mortgage amount, which is \$[/tex]300,000.
5. Calculate the Annual Percentage Rate (APR):
The formula for APR is:
[tex]\[ \text{APR} = \left(\frac{2 \times \text{Total Interest}}{\text{Principal} \times (\text{Number of years} + 1)}\right) \][/tex]
Plugging in the values:
[tex]\[ \text{APR} = \left(\frac{2 \times 60,000}{300,000 \times (30 + 1)}\right) \][/tex]
6. Perform the calculation:
- Calculate the denominator: [tex]\(300,000 \times 31 = 9,300,000\)[/tex]
- Calculate the numerator: [tex]\(2 \times 60,000 = 120,000\)[/tex]
- Divide the numerator by the denominator:
[tex]\[ \frac{120,000}{9,300,000} \approx 0.0129032258 \][/tex]
7. Convert the APR to a percentage:
[tex]\[ \text{APR percentage} = 0.0129032258 \times 100 \approx 1.29032258\% \][/tex]
8. Round the APR to the nearest tenth:
The APR, when rounded to the nearest tenth, is approximately 1.3%.
### Final Result:
The APR for Brad Henderson's mortgage is approximately 1.3%.
Thus, the correct answer from the given options is:
[tex]\[ \boxed{1.3\%} \][/tex]
1. Identify the given information:
- Mortgage amount (Principal): \[tex]$300,000 - Monthly payment: \$[/tex]1,000
- Total interest paid over the loan duration: \[tex]$60,000 - Duration of the loan: 30 years 2. Calculate the total number of payments: \[\text{Number of years} \times 12 = 30 \text{ years} \times 12 = 360 \text{ payments}\] 3. Calculate the total repayment amount: \[\text{Monthly payment} \times \text{Number of payments} = \$[/tex]1,000 \times 360 = \[tex]$360,000\] 4. Calculate the amount paid towards the principal: This is essentially the mortgage amount, which is \$[/tex]300,000.
5. Calculate the Annual Percentage Rate (APR):
The formula for APR is:
[tex]\[ \text{APR} = \left(\frac{2 \times \text{Total Interest}}{\text{Principal} \times (\text{Number of years} + 1)}\right) \][/tex]
Plugging in the values:
[tex]\[ \text{APR} = \left(\frac{2 \times 60,000}{300,000 \times (30 + 1)}\right) \][/tex]
6. Perform the calculation:
- Calculate the denominator: [tex]\(300,000 \times 31 = 9,300,000\)[/tex]
- Calculate the numerator: [tex]\(2 \times 60,000 = 120,000\)[/tex]
- Divide the numerator by the denominator:
[tex]\[ \frac{120,000}{9,300,000} \approx 0.0129032258 \][/tex]
7. Convert the APR to a percentage:
[tex]\[ \text{APR percentage} = 0.0129032258 \times 100 \approx 1.29032258\% \][/tex]
8. Round the APR to the nearest tenth:
The APR, when rounded to the nearest tenth, is approximately 1.3%.
### Final Result:
The APR for Brad Henderson's mortgage is approximately 1.3%.
Thus, the correct answer from the given options is:
[tex]\[ \boxed{1.3\%} \][/tex]
