Suppose that you took out a loan at 7% interest for 192 days. If the amount of interest was $149.33, use the ordinary interest method to find the amount of principal you borrowed. Round to the nearest whole dollar amount.
$
I = PRT
149.33 = P * 0.07 * 0.5260
149.33 = 0.0368P
149.33 / 0.0368 = P
4057.88 = 4058 = P
To find the amount of principal borrowed using the ordinary interest method, we can use the formula:
Interest = (Principal) x (Interest Rate) x (Time in years)
First, we need to convert the time from days to years. We know that there are 365 days in a year, so we divide the number of days by 365:
Time in years = 192 days / 365 days/year
Next, we can rearrange the formula to solve for the principal:
Principal = Interest / (Interest Rate x Time in years)
Let's plug in the given values into the formula:
Interest = $149.33
Interest Rate = 7% = 0.07 (expressed as a decimal)
Time in years = 192 days / 365 days/year
Calculating the time in years:
Time in years = 192 / 365
Now we can substitute the values into the formula:
Principal = $149.33 / (0.07 x (192 / 365))
Now we just need to calculate the expression:
Principal = $149.33 / (0.07 x (192 / 365))
Principal = $149.33 / (0.07 x 0.526)
Principal = $149.33 / 0.03682
Principal ≈ $4051.11 (rounded to two decimal places)
Therefore, the approximate amount of principal borrowed is $4,051.