To determine which loan has the lowest total payback, we need to calculate the total payback amount for both Loan A and Loan B. The total payback is the sum of the principal and the interest paid over the loan period.
Loan A:
- Principal: $4,500
- Interest Rate: 5%
- Time: 3 years
Interest can be calculated using the formula: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
For Loan A: \[ \text{Interest} = 4,500 \times 0.05 \times 3 = 4,500 \times 0.15 = 675 \] Total payback for Loan A: \[ \text{Total Payback} = \text{Principal} + \text{Interest} = 4,500 + 675 = 5,175 \]
Loan B:
- Principal: $4,300
- Interest Rate: 6%
- Time: 3 years
For Loan B: \[ \text{Interest} = 4,300 \times 0.06 \times 3 = 4,300 \times 0.18 = 774 \] Total payback for Loan B: \[ \text{Total Payback} = \text{Principal} + \text{Interest} = 4,300 + 774 = 5,074 \]
Comparison:
- Total Payback for Loan A: $5,175
- Total Payback for Loan B: $5,074
Conclusion: Loan B will have the lowest total payback because the total of the principal and the interest paid for Loan B ($5,074) is less than the same total for Loan A ($5,175).
So the correct statement is: "Loan B will have the lowest total payback because the total of the principal and the interest paid for loan B is less than the same total for loan A."
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