You are expecting a tax refund of $4,000 in 4 weeks. A tax preparer offers you an "interest-free" loan of $4,000 for a fee of $50 to be repaid by your refund check when it arrives in 4 weeks. Thinking of the fee as interest, what simple interest rate would you be paying on this loan?
let the rate be r
4000(r)(4/52) = 50
r = 50(52)/((4000)(4))
= .165 or 16.5%
There are actual companies dealing in paycheck-bridge loans that are charging $10 per week for a $200 quick "paycheck loan"
that is a rate of ...
200(r)(1/52) = 10
r = 10(52)/200 = 2.6 or 260%
To determine the simple interest rate, you need to consider the fee of $50 as the interest paid on the loan amount of $4,000.
The formula to calculate simple interest is:
Interest = Principal × Rate × Time
In this case, the interest is equal to the fee, which is $50. The principal is the loan amount of $4,000. The time is the duration of the loan in years, which is 4 weeks, or 4/52 years.
Plugging in these values into the formula, we have:
50 = 4000 × Rate × (4/52)
Next, to find the interest rate, we need to isolate the rate variable. Rearranging the equation, we have:
Rate = 50 / (4000 × (4/52))
Simplifying further, we get:
Rate = 52 × 50 / (4000 × 4)
Calculating the numerator first, we have:
52 × 50 = 2600
Now, calculating the denominator:
4000 × 4 = 16000
Finally, dividing the numerator by the denominator:
Rate = 2600 / 16000
This simplifies to:
Rate = 0.1625
Therefore, you would be paying an interest rate of approximately 0.1625, or 16.25% on this loan if you consider the fee as interest.
To calculate the simple interest rate you would be paying on this loan, we can use the formula:
Simple Interest = (Fee / Principal) * (100 / Time)
In this case:
- Fee = $50
- Principal = $4,000
- Time = 4 weeks
Let's plug in the values and calculate the simple interest rate:
Simple Interest = (50 / 4000) * (100 / 4) = (0.0125) * 25 = 0.3125
So, the simple interest rate you would be paying on this loan is 0.3125, or 31.25%.