Alex needed proceeds of $12,345. How much does he need to take out at 6% interest for 120 days to receive proceeds of $12,345?
Ao = Ar + Ar*r*t,
Ao = 12,345 + 12,345*(0.06/360)*120 = $12,591.90 = Amt. owed or taken out.
To find out how much Alex needs to take out at 6% interest for 120 days in order to receive proceeds of $12,345, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Here, the Principal is the amount Alex needs to take out, the Rate is 6% (or 0.06 as a decimal), and the Time is 120 days (or 120/365 as a fraction of a year).
Let's denote the Principal as P. We can set up the equation as follows:
12,345 = P * 0.06 * (120/365)
To solve for P, we can isolate it on one side of the equation. We can start by dividing both sides by 0.06 * (120/365):
P = 12,345 / (0.06 * (120/365))
Now, we can simplify the expression in parentheses:
P = 12,345 / (0.06 * 120/365)
Dividing 0.06 by 120 and multiplying by 365, we get:
P = 12,345 / 0.0185
Evaluating the division, we find:
P ≈ $668,918.92
So, Alex needs to take out approximately $668,918.92 at 6% interest for 120 days to receive proceeds of $12,345.