Final answer:
Michelle would need to pay approximately $3,287.50 to clear the loan on June 19, 2015, with a simple interest rate of 2.50% per annum. This amount is determined by using the simple interest formula and accounting for the time period from June 19, 2015, to August 17, 2015, which is roughly 2 months. The options given in the question do not match this answer, which suggests the need for reevaluation of the problem or provided details.
Step-by-step explanation:
Michelle was required to repay a loan that matured to $3,300 on August 17, 2015. She decided to pay off the loan on June 19, 2015, instead. To calculate how much she would need to pay on June 19, you have to know the simple interest rate, which in this case is 2.50% per annum (p.a.).
The formula for calculating the amount owed on a loan with simple interest is:
A = P(1 + rt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of the loan).
- r is the annual interest rate (decimal).
- t is the time the money is invested for, in years.
First, we need to find out how many years have passed from June 19 to August 17. That is, from June 19, 2015, to August 17, 2015. This period amounts to approximately 2 months or about ⅓ of a year.
To find out the principal P, we rearrange the formula as follows:
P = A / (1 + rt)
Using the given information:
P = $3,300 / (1 + 0.025 × ⅓)
P = $3,300 / (1 + 0.025 × 0.1667)
P = $3,300 / (1 + 0.0041675)
P = $3,300 / 1.0041675
P ≈ $3,287.50
Therefore, Michelle would have to pay approximately $3,287.50 to clear the loan on June 19, 2015. This is not one of the options provided, indicating there may have been a mistake either with the question details or the calculation. A reevaluation of the original problem, the options given, or the interest details may be necessary to provide an accurate answer.