To determine the Annual Percentage Rate (APR) for John Blake's mortgage, we will break down the provided information and follow a systematic approach to find the APR.
1. Given Information:
- Principal amount (loan) = \[tex]$80,000
- Loan term = 30 years
- Monthly payment = \$[/tex]600
- Total interest paid = \$136,000
2. Total Amount Paid Over the Loan Term:
The total amount paid over the life of the loan includes both the principal and the total interest paid:
[tex]\[
\text{Total amount paid} = \text{Monthly payment} \times 12 \times \text{Loan term in years}
\][/tex]
Using the provided information:
[tex]\[
\text{Total amount paid} = 600 \times 12 \times 30 = 216,000
\][/tex]
3. Total Interest Paid:
The total interest paid over the life of the loan is given as:
[tex]\[
\text{Total interest paid} = 136,000
\][/tex]
4. Total Repayment Amount:
The total amount repaid over the life of the loan includes both the principal and the total interest paid:
[tex]\[
\text{Total repayment amount} = \text{Principal} + \text{Total interest paid}
\][/tex]
Using the provided information:
[tex]\[
\text{Total repayment amount} = 80,000 + 136,000 = 216,000
\][/tex]
5. Monthly Interest Rate Approximation:
To find the monthly interest rate, we use the relationship between the total interest paid, the principal amount, and the loan term. The approximation can be calculated as:
[tex]\[
\text{Monthly interest rate} = \frac{\text{Total interest paid}}{\text{Principal amount} \times \text{Loan term in months}}
\][/tex]
Where the loan term in months is:
[tex]\[
\text{Loan term in months} = 30 \times 12 = 360
\][/tex]
Using the provided information:
[tex]\[
\text{Monthly interest rate} \approx \frac{136,000}{80,000 \times 360} = \frac{136,000}{28,800,000} \approx 0.004722 \quad \text{(approximately)}
\][/tex]
6. Annual Percentage Rate (APR):
Finally, the APR is calculated by converting the monthly interest rate to an annual rate:
[tex]\[
\text{APR} = \text{Monthly interest rate} \times 12 \times 100
\][/tex]
Using the monthly interest rate approximation:
[tex]\[
\text{APR} \approx 0.004722 \times 12 \times 100 = 5.666666666666667
\][/tex]
Thus, the APR for John Blake's mortgage is approximately:
[tex]\[
\boxed{5.67\%}
\][/tex]
