Answer :
Certainly! Let's work through this step-by-step to find out how much Mo borrowed to buy the car using the information given in the problem.
### Step-by-Step Solution:
1. Identify the given information:
- Total interest paid: [tex]$7,683.20 - Loan period (Time): 5 years - Simple interest formula: Interest = Principal Rate Time 2. Understand what needs to be found: - Principal amount (P): This is the amount Mo originally borrowed. 3. Assume the interest rate: - Since the interest rate is not provided, we need to assume a reasonable annual interest rate. For this example, let's assume an annual interest rate of 5% (or 0.05 as a decimal). 4. Use the formula for simple interest: - The formula for simple interest is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] - Rearrange the formula to solve for the Principal: \[ \text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}} \] 5. Substitute the given values and assume rate: - Interest (I) = $[/tex]7,683.20
- Rate (R) = [tex]\(0.05\)[/tex]
- Time (T) = 5 years
- Thus, the formula becomes:
[tex]\[ \text{Principal} = \frac{7,683.20}{0.05 \times 5} \][/tex]
6. Calculate the principal:
- Multiply the rate and the time:
[tex]\[ 0.05 \times 5 = 0.25 \][/tex]
- Divide the interest by the product of the rate and the time:
[tex]\[ \text{Principal} = \frac{7,683.20}{0.25} = 30,732.80 \][/tex]
### Conclusion:
Mo borrowed [tex]$30,732.80 to buy the car. So, the principal amount Mo borrowed is $[/tex]30,732.80.
### Step-by-Step Solution:
1. Identify the given information:
- Total interest paid: [tex]$7,683.20 - Loan period (Time): 5 years - Simple interest formula: Interest = Principal Rate Time 2. Understand what needs to be found: - Principal amount (P): This is the amount Mo originally borrowed. 3. Assume the interest rate: - Since the interest rate is not provided, we need to assume a reasonable annual interest rate. For this example, let's assume an annual interest rate of 5% (or 0.05 as a decimal). 4. Use the formula for simple interest: - The formula for simple interest is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] - Rearrange the formula to solve for the Principal: \[ \text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}} \] 5. Substitute the given values and assume rate: - Interest (I) = $[/tex]7,683.20
- Rate (R) = [tex]\(0.05\)[/tex]
- Time (T) = 5 years
- Thus, the formula becomes:
[tex]\[ \text{Principal} = \frac{7,683.20}{0.05 \times 5} \][/tex]
6. Calculate the principal:
- Multiply the rate and the time:
[tex]\[ 0.05 \times 5 = 0.25 \][/tex]
- Divide the interest by the product of the rate and the time:
[tex]\[ \text{Principal} = \frac{7,683.20}{0.25} = 30,732.80 \][/tex]
### Conclusion:
Mo borrowed [tex]$30,732.80 to buy the car. So, the principal amount Mo borrowed is $[/tex]30,732.80.
