Final answer:
The formula for simple interest is I = prt, and to solve for the interest rate r, Michael should rearrange the formula to r = I / (pt), which is option a. Using this formula, if Michael owes $500 in interest on a $10,000 loan over 5 years, the interest rate would be 1%.
Step-by-step explanation:
The formula for simple interest is I = prt, where I stands for the interest earned, p is the principal amount, r is the rate of interest, and t is the time period in years. Michael wants to rearrange the formula to solve for the interest rate r. By isolating r on one side, he derives the formula: r = I / (pt).
This manipulation is straightforward algebra. First, we would normally divide both sides of the original equation by p and t which would give us r = I / (pt). Therefore, Michael should use option a. r = I / (pt) to calculate the interest rate.
As an example, let's say Michael borrowed $10,000 at a simple interest rate and after 5 years he owes $500 in interest. We would calculate the rate as follows:
Interest I = $500
Principal p = $10,000
Time t = 5 years
Rate r = $500 / ($10,000 × 5)
Rate r = $500 / $50,000
Rate r = 0.01 or 1%
Therefore, the interest rate is 1%.