Matty Kaminsky owns a new Volvo. His June monthly interest was $400. The rate is 8 1/2 percent. Matty's principal balance at the beginning of June, rounded to the nearest cent, is: (Use 360 days)
I = Po*r*t = 400
Po*(8.5/360)*30days = 400
0.70833*Po = 400
Po = $564.71
4564.71.
To find the principal balance at the beginning of June, we need to use the formula:
Interest = Principal Balance x Interest Rate x Time
In this case, the interest is given ($400), the interest rate is 8 1/2 percent (or 0.085), and the time is 1 month (since it is a monthly interest).
Let's assume x represents the principal balance. We can now set up the equation:
$400 = x * 0.085 * (1/12)
Simplifying the equation:
$400 = x * (0.085/12)
To find x, we need to divide both sides of the equation by (0.085/12):
$400 / (0.085/12) = x
Calculating:
$400 / (0.085/12) = x
$400 / 0.00708 = x
$56,497.18 ≈ x
Therefore, Matty's principal balance at the beginning of June, rounded to the nearest cent, is $56,497.18.
To calculate Matty Kaminsky's principal balance at the beginning of June, we need to use the formula for simple interest:
Interest = Principal * Rate * Time
In this case, we know that the interest is $400 and the rate is 8 1/2 percent, or 8.5%. We also need to know the time period for calculating the interest.
The time period for interest is usually given in years. However, in this case, it is mentioned that we should use 360 days. This suggests that we're working with a 360-day year, commonly used in financial calculations.
To calculate the principal, we rearrange the formula as follows:
Principal = Interest / (Rate * Time)
First, we need to convert the rate from a percent to a decimal by dividing it by 100. So, the rate becomes 0.085.
Next, we need to determine the time period in years. Since we are given the interest for the month of June, and we are using a 360-day year, the time period in years is 30/360, which equals 1/12.
Now we can substitute the values into the formula:
Principal = $400 / (0.085 * 1/12)
To simplify, multiply 0.085 by 12:
Principal = $400 / (1.02)
Finally, perform the division:
Principal = $392.16
So, Matty Kaminsky's principal balance at the beginning of June, rounded to the nearest cent, is $392.16.