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Brad Henderson takes out a mortgage for [tex]$\$[/tex]300,000[tex]$. This is a 30-year loan at $[/tex]\[tex]$1,000$[/tex] per month, with a total interest of [tex]$\$[/tex]60,000[tex]$.

What is the APR using the formula (to the nearest tenth)?

$[/tex]APR = \qquad \%$

A. 33.2%
B. 3.3%
C. 13.2%
D. 1.3%


Sagot :

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]