Jay Jenkins takes out a 12.5% simple interest loan today that will be repaid 9 months from now with a payoff amount of $5000.00. What amount is Jay borrowing?
Let X be the amount Jay is borrowing.
The interest on the loan is X * 0.125 * (9/12) = X * 0.09375.
So Jay is borrowing X + X * 0.09375 = $5000.
Thus (1 + 0.09375) * X = $5000.
Thus (1.09375) * X = $5000.
Thus X = $5000 / 1.09375 = $4568.97 rounded to $$4569. Answer: \boxed{4569}.
To find the amount Jay is borrowing, we need to calculate the interest accrued and add it to the payoff amount.
Step 1: Calculate the interest accrued
Interest = Principal * Interest Rate * Time
Here, the interest rate is 12.5% = 0.125 (in decimal form), and the time is 9 months.
Interest = Principal * 0.125 * 9
Step 2: Add the interest accrued to the payoff amount
Total Amount = Principal + Interest = Principal + (Principal * 0.125 * 9)
Total Amount = $5000
We can solve this equation to find the Principal.
Principal + (Principal * 0.125 * 9) = $5000
Principal + 1.125 * Principal = $5000
Principal (1 + 1.125) = $5000
Principal * 2.125 = $5000
Principal = $5000 / 2.125
Therefore, the amount Jay is borrowing is $2352.94 (rounded to two decimal places).
To find out the amount Jay is borrowing, we need to use the simple interest formula:
Interest = Principal x Rate x Time
In this case, we know the following information:
Rate = 12.5% = 0.125 (as a decimal)
Time = 9 months
To solve for the Principal (the amount Jay is borrowing), we rearrange the formula:
Principal = Interest / (Rate x Time)
First, calculate the interest:
Interest = Payoff amount - Principal
Given that the payoff amount is $5000.00, we can rewrite the above equation as:
Interest = $5000.00 - Principal
Now, we can substitute the values into the interest formula:
Interest = Principal x Rate x Time
In this case, Principal = x (unknown)
Interest = x * 0.125 * 9 months
Substituting the above values into the equation:
$5000.00 - x = x * 0.125 * 9
Let's solve for x:
$5000.00 - x = 1.125x
We can rearrange this equation as:
1.125x + x = $5000.00
Combine like terms:
2.125x = $5000.00
Divide both sides by 2.125:
x = $5000.00 / 2.125
Calculating the right side of the equation:
x = $2352.94 (rounded to two decimal places)
Therefore, Jay is borrowing approximately $2352.94.