Answer :
To determine the Annual Percentage Rate (APR), we need to follow these steps:
1. Identify the principal loan amount:
[tex]\[ \text{Loan Amount} = \$300{,}000 \][/tex]
2. Calculate the total payments over the life of the loan:
[tex]\[ \text{Total Monthly Payments} = 30 \text{ years} \times 12 \text{ months/year} \times \$1{,}000/\text{month} = \$360{,}000 \][/tex]
3. Identify the total interest paid over the life of the loan:
[tex]\[ \text{Total Interest Paid} = \$60{,}000 \][/tex]
4. Calculate the total amount paid by the end of the mortgage term:
[tex]\[ \text{Total Amount Paid} = \text{Loan Amount} + \text{Total Interest Paid} = \$300{,}000 + \$60{,}000 = \$360{,}000 \][/tex]
5. Determine the total interest paid as a proportion of the loan amount:
[tex]\[ \text{Interest Proportion} = \frac{\text{Total Interest Paid}}{\text{Loan Amount}} = \frac{\$60{,}000}{\$300{,}000} = 0.2 \][/tex]
6. Calculate the APR, considering a 30-year loan period:
[tex]\[ \text{APR} = \left(\text{Interest Proportion} \times \frac{100}{30}\right) = 0.2 \times \frac{100}{30} = \frac{20}{30} \approx 0.6667 \% \text{ annually} \][/tex]
The result in percentage form:
[tex]\[ \text{APR} = 0.6667 \% \][/tex]
Rounding to the nearest tenth, the Annual Percentage Rate (APR) is:
[tex]\[ \boxed{0.7 \%} \][/tex]
1. Identify the principal loan amount:
[tex]\[ \text{Loan Amount} = \$300{,}000 \][/tex]
2. Calculate the total payments over the life of the loan:
[tex]\[ \text{Total Monthly Payments} = 30 \text{ years} \times 12 \text{ months/year} \times \$1{,}000/\text{month} = \$360{,}000 \][/tex]
3. Identify the total interest paid over the life of the loan:
[tex]\[ \text{Total Interest Paid} = \$60{,}000 \][/tex]
4. Calculate the total amount paid by the end of the mortgage term:
[tex]\[ \text{Total Amount Paid} = \text{Loan Amount} + \text{Total Interest Paid} = \$300{,}000 + \$60{,}000 = \$360{,}000 \][/tex]
5. Determine the total interest paid as a proportion of the loan amount:
[tex]\[ \text{Interest Proportion} = \frac{\text{Total Interest Paid}}{\text{Loan Amount}} = \frac{\$60{,}000}{\$300{,}000} = 0.2 \][/tex]
6. Calculate the APR, considering a 30-year loan period:
[tex]\[ \text{APR} = \left(\text{Interest Proportion} \times \frac{100}{30}\right) = 0.2 \times \frac{100}{30} = \frac{20}{30} \approx 0.6667 \% \text{ annually} \][/tex]
The result in percentage form:
[tex]\[ \text{APR} = 0.6667 \% \][/tex]
Rounding to the nearest tenth, the Annual Percentage Rate (APR) is:
[tex]\[ \boxed{0.7 \%} \][/tex]
