What is the maximum amount Ginger Logan can borrow today if it must be repaid in 13 months with simple interest at $8 \%$ and she knows that at the time she will be able to repay no more than $\$ 36,000$ ? She can borrow $\$ \square$. (Round to the nearest dollar as needed.)
Solution
Step 1 ：We are given that Ginger Logan can repay no more than $36,000 in 13 months with a simple interest rate of 8%.
Step 2 ：The total repayment amount is the sum of the principal and the interest. So, we need to adjust our formula to account for this. The new formula becomes \(P = \frac{Total}{1 + RT}\).
Step 3 ：We can substitute the given values into this formula to find the maximum amount that can be borrowed. Here, Total = $36,000, Rate = 8% or 0.08, and Time = 13 months or approximately 1.0833 years.
Step 4 ：Substituting these values into the formula, we get \(P = \frac{36000}{1 + 0.08 \times 1.0833}\).
Step 5 ：Solving this equation, we find that the maximum amount that can be borrowed is approximately $33,128.83.
Step 6 ：Rounding this to the nearest dollar, we get $33,129.
Step 7 ：So, the maximum amount Ginger Logan can borrow today is \(\boxed{33,129}\) dollars.
