You buy some furniture for $600. The department store offers you “no interest for 8 months” after which you can pay the $600 in one lump sum. To take advantage of this deal, the store charges a $25 service fee, which is to be paid today. What rate of simple interest is the store charging you for this “no interest” loan?
I am completely lost with this question.
This is what I have tried but I'm pretty sure it is wrong.
FV=PV(1+r)^n
600=600 (1+r)^(0.67)
r= 0.04166
I = PRT
25 = 600 * R * 0.667
25 / 400.2R
25/400.2 = R
R = 0.06247 = 6.25%
To find the rate of simple interest in this scenario, we need to consider the information provided in the question.
First, let's determine the amount you will owe after 8 months. Since the deal offers "no interest for 8 months," the total amount payable will be the same as the purchase price, $600.
Next, let's calculate the total cost by considering the service fee. In addition to the furniture price, you need to pay a $25 service fee today. Therefore, the total amount payable will be $600 (furniture price) + $25 (service fee) = $625.
From this information, we can conclude that the amount of interest charged by the store is $625 - $600 = $25, which is equal to the service fee.
Now we can calculate the interest rate (r). We can use the simple interest formula:
Simple Interest = Principal (P) * Rate (r) * Time (t)
In this case, the principal (P) is $600, the time (t) is 8 months, and the simple interest is $25. Substituting these values into the formula gives us:
25 = 600 * r * (8/12)
To simplify further, we convert the time of 8 months to years (8/12).
25 = 600 * r * (2/3)
Next, we can isolate the interest rate (r) by dividing both sides of the equation by 600 * (2/3):
r = 25 / (600 * 2/3)
r = 25 / (400/3)
r = 25 * (3/400)
r = 0.1875
Therefore, the rate of simple interest charged by the store for this "no interest" loan is approximately 0.1875 or 18.75%.
Note: It is important to remember that in a "no interest" loan, there could still be other fees or charges involved, like the service fee in this case.