Janet got 671.50 in cash as the proceeds form a loan of $680. The discount rate was 10% simple interest. Find the discount period. I got 118.5 months but am not sure if I did it correctly.
I do not understand why 10% loan interest would be called a "discount rate". Why was the cash received less than the loan amount? Were "points' added to the loan? Are payments made monthly? Is Janet the loaner or the borrower?
This is all the info I got in the question and is probably why I don't really understand what to do with it. Thanks anyway!
To find the discount period, we need to use the concept of simple interest. The formula for simple interest is:
Interest = Principal * Rate * Time
In this case, the Principal (P) is the loan amount, which is $680. The Rate (R) is the discount rate, which is 10% expressed as a decimal, so it is 0.10. We want to find the Time (T), which represents the discount period.
The problem states that Janet received $671.50 in cash as the proceeds from the loan. This means that the interest she paid was $680 - $671.50 = $8.50.
Now, we can plug in the values into the formula and solve for Time:
$8.50 = $680 * 0.10 * T
To solve for T, divide both sides of the equation by ($680 * 0.10):
$8.50 / ($680 * 0.10) = T
T = 0.0125
The discount period is often expressed in years, so multiply T by 12 to convert it to months:
T = 0.0125 * 12 = 0.15 months
Therefore, the discount period is approximately 0.15 months, which is equivalent to 0.15 * 30 = 4.5 days.
So, the correct answer is approximately 4.5 days, not 118.5 months.