Which formula do I use for the following question: Sheila Spinney borrowed $32,500 at 7.5% simple interest for 180 days on January 7. The bank later sold the note at an 8% discount on March 2. Find the proceeds to the bank.
To find the proceeds to the bank, we need to calculate two things: the interest earned by Sheila Spinney, and the discount given when the bank sold the note.
First, let's calculate the interest earned by Sheila Spinney. The formula for simple interest is:
Interest = Principal x Rate x Time
In this case, the principal amount borrowed is $32,500, the rate is 7.5%, and the time is 180 days. To calculate the interest earned, we can plug in these values into the formula:
Interest = $32,500 x 0.075 x (180/365)
Simplifying this calculation, we get:
Interest = $1,269.86 (rounded to two decimal places)
Next, let's calculate the discount given when the bank sold the note. The discount is given as a percentage of the note value, which is the principal plus the interest earned. In this case, the note value is $32,500 + $1,269.86 = $33,769.86.
To calculate the discount, we multiply the note value by the discount rate. In this case, the discount rate is 8%. Converting the percentage to a decimal, we get 0.08. So, the discount is:
Discount = $33,769.86 x 0.08
Simplifying this calculation, we get:
Discount = $2,701.59 (rounded to two decimal places)
Finally, to find the proceeds to the bank, we subtract the discount from the note value:
Proceeds = Note value - Discount
Proceeds = $33,769.86 - $2,701.59
Simplifying this calculation, we get:
Proceeds = $31,068.27 (rounded to two decimal places)
Therefore, the proceeds to the bank are $31,068.27.