To determine which option results in the least amount of interest paid, we can calculate the total interest for each repayment period using the formula for simple interest, which is:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
Where:
- Principal is the initial balance
- Rate is the annual percentage rate (as a decimal)
- Time is the time period in years
Given:
- Principal = $5810
- APR = 16.2% = 0.162
We will calculate the interest for each repayment period in months and convert it into years by dividing by 12.
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For 13 months: \[ \text{Time} = \frac{13}{12} \approx 1.0833 \text{ years} \] \[ \text{Interest} = 5810 \times 0.162 \times 1.0833 \approx 1,020.92 \]
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For 9 months: \[ \text{Time} = \frac{9}{12} = 0.75 \text{ years} \] \[ \text{Interest} = 5810 \times 0.162 \times 0.75 \approx 706.41 \]
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For 11 months: \[ \text{Time} = \frac{11}{12} \approx 0.9167 \text{ years} \] \[ \text{Interest} = 5810 \times 0.162 \times 0.9167 \approx 872.43 \]
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For 7 months: \[ \text{Time} = \frac{7}{12} \approx 0.5833 \text{ years} \] \[ \text{Interest} = 5810 \times 0.162 \times 0.5833 \approx 561.05 \]
Now, summarizing the interest paid for each option:
- 13 months: $1,020.92
- 9 months: $706.41
- 11 months: $872.43
- 7 months: $561.05
From these calculations, the repayment period of 7 months results in the least amount of interest paid at approximately $561.05.