if you paid $120 to a loan company for the use of $2000 for 90 days, what annual rate of interest did they charge?

I = PRT

120 = 2,000 * R * 0.25

120 = 500R

0.24 - 24% = R

.24

Well, let's see. If you paid $120 for the use of $2000 for 90 days, we can calculate the interest first.

The total interest paid is $120.

Now, let's convert the interest amount to an annual rate.

If you paid $120 for 90 days, we can calculate the daily interest rate:

$120 / 90 = $1.33 per day.

Now, there are 365 days in a year, so we can calculate the annual interest rate:

$1.33 per day * 365 days = $485.45.

Therefore, the annual rate of interest charged by the loan company is a whopping $485.45! That's enough to make your bank account do a little dance.

To determine the annual rate of interest charged by the loan company, you can follow these steps:

Step 1: Calculate the total interest paid for the 90-day loan period.
Interest = Total payment - Loan amount
Interest = $120 - $2000
Interest = -$1880

Step 2: Calculate the daily interest rate.
Daily interest rate = Total interest / Number of days
Daily interest rate = -$1880 / 90
Daily interest rate = -$20.89

Step 3: Calculate the annual interest rate.
Annual interest rate = Daily interest rate * 365
Annual interest rate = -$20.89 * 365
Annual interest rate = - $7,610.85

Since the negative annual interest rate doesn't make sense in this context, it is likely that there was an error or additional fees involved in the calculation.

To find the annual rate of interest charged by the loan company, we can use the following formula:

Interest = (Principal × Rate × Time)/100

Let's first calculate the interest paid for the 90-day period using the given information:

Interest = 120 (paid amount) - 2000 (principal) = -1880

Since the interest is negative, it means that you paid $1880 less than the borrowed amount. Therefore, we need to adjust the principal accordingly:

Adjusted Principal = Principal - Interest
Adjusted Principal = 2000 - (-1880)
Adjusted Principal = 2000 + 1880
Adjusted Principal = 3880

Now we can find the annual rate of interest. We know the adjusted principal, and the time is given in terms of days. But we need to convert it to a yearly basis. There are 365 days in a year, so:

Rate = (Interest × 100)/(Adjusted Principal × Time)
Rate = (-1880 × 100)/(3880 × 90/365)
Rate = -188000/(3880 × 90/365)
Rate = -188000/(97.939)
Rate ≈ -1918.44

The negative sign indicates that the interest charged by the loan company is an annualized percentage deduction from the principal. So, they charged approximately 1918.44% annual interest.

Please note: The negative interest rate in this case suggests that either the question is posed in reverse (stating payment rather than interest earned), or the loan company is providing an interest subsidy or discount.