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8 Multiple Choice 1 point If a loan charges 1% interest per month, what is its APR? 1% 1.68% 12% 12.68%

Problemas

8
Multiple Choice 1 point
If a loan charges 1%  interest per month, what is its APR?
1% 
1.68% 
12% 
12.68%

8 Multiple Choice 1 point If a loan charges 1% interest per month, what is its APR? 1% 1.68% 12% 12.68%

Solución

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Anaísmaestro · Tutor durante 5 años
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To calculate the Annual Percentage Rate (APR) from a monthly interest rate, we need to compound the monthly rate over 12 months. The formula to convert a monthly interest rate to an APR is:<br /><br />\[ \text{APR} = (1 + \text{Monthly Rate})^{12} - 1 \]<br /><br />Given the monthly interest rate is \(1\%\) or \(0.01\) in decimal form, we can plug this into the formula:<br /><br />\[ \text{APR} = (1 + 0.01)^{12} - 1 \]<br /><br />First, calculate \( (1 + 0.01)^{12} \):<br /><br />\[ (1 + 0.01)^{12} = 1.01^{12} \]<br /><br />Using a calculator:<br /><br />\[ 1.01^{12} \approx 1.126825 \]<br /><br />Now, subtract 1 from this result to find the APR:<br /><br />\[ \text{APR} = 1.126825 - 1 = 0.126825 \]<br /><br />Convert the decimal form back to a percentage:<br /><br />\[ \text{APR} \approx 12.6825\% \]<br /><br />Rounding to two decimal places, the APR is approximately \(12.68\%\).<br /><br />Therefore, the correct answer is:<br /><br />\[ \boxed{12.68\%} \]
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