To determine the principal that will earn $67.14 interest at an annual interest rate of 6.25% for 82 days, we can use the simple interest formula:

$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$

Where:

• Interest = $67.14
• Rate = 6.25% per year, or 0.0625 as a decimal
• Time = 82 days (since the interest rate is annual, we convert time into years: $\frac{82}{365}$)

Rearranging the formula to solve for Principal:

$\text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}}$

Substituting the given values:

$\text{Principal} = \frac{67.14}{0.0625 \times \frac{82}{365}}$

Now, let's calculate it:

$\text{Principal} = \frac{67.14}{0.0625 \times 0.22466} = \frac{67.14}{0.01404125} \approx 4779.27$

So, the principal is approximately $4,779.27.

Would you like any further details or have any questions?

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Here are 8 related questions that expand on this topic:

1. How would the principal change if the interest rate were 7.5%?
2. What would be the interest earned if the principal were $5,000 at the same interest rate and time period?
3. How does compounding affect the interest earned in comparison to simple interest?
4. What is the formula for compound interest, and how does it differ from simple interest?
5. How many days would it take to earn $100 interest with the same principal and rate?
6. What would the principal be if the interest rate were compounded monthly?
7. How does the length of time affect the total interest earned?
8. Can you explain how to calculate the time required to double the principal using the Rule of 72?

Tip: Always convert time into years when using an annual interest rate in simple interest calculations.