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.
Well, it seems like Sheila was in quite a 'spinney' situation, borrowing money at a 7.5% interest rate. Now, let's calculate the proceeds to the bank after their generous discount.
To find the interest owed by Sheila on her loan for 180 days, we can use the formula: interest = principal * rate * time. Plugging in the values, we have: interest = $32,500 * 0.075 * (180/365).
Let's do some math! The interest turns out to be approximately $1,003.42.
Now, to calculate the sale price of the note after the bank's 8% discount, we simply multiply the principal by (1 - discount rate). In this case, the discounted price is $32,500 * (1 - 0.08).
Let's crunch the numbers again! The sale price of the note is $29,900.
Therefore, the proceeds to the bank would be the sale price minus the interest owed: $29,900 - $1,003.42.
After all this calculating, we find that the proceeds to the bank would be approximately $28,896.58.
So, it seems like the bank managed to 'spin' a profit even after applying a discount.
To find the proceeds to the bank, we need to calculate the total interest and the discounted amount.
Step 1: Calculate the total interest.
The formula to calculate simple interest is:
Interest = Principal * Rate * Time
In this case, Sheila borrowed $32,500 at a rate of 7.5% for 180 days.
Interest = $32,500 * 0.075 * (180/365)
Interest = $1,267.12
Step 2: Calculate the discounted amount.
The discount is given as 8%.
Discount = Principal * Discount Rate
Discount = $32,500 * 0.08
Discount = $2,600
Step 3: Calculate the proceeds to the bank.
The proceeds to the bank can be calculated using the formula:
Proceeds = Principal - Interest - Discount
Proceeds = $32,500 - $1,267.12 - $2,600
Proceeds = $28,632.88
Therefore, the proceeds to the bank are $28,632.88.
To find the proceeds to the bank, we need to calculate the amount of interest Sheila owes and subtract the discount from the original loan amount.
First, let's calculate the interest that Sheila owes:
Interest = Principal × Rate × Time
Principal = $32,500
Rate = 7.5% or 0.075 (decimal form)
Time = 180 days
Interest = $32,500 × 0.075 × (180/365)
Next, we'll calculate the discount:
Discount = Principal × Discount Rate
Since the bank sold the note at an 8% discount, we can convert the discount rate to decimal form:
Discount Rate = 8% or 0.08
Discount = $32,500 × 0.08
Finally, we can calculate the proceeds to the bank by subtracting the discount from the loan amount:
Proceeds = Principal - Discount
Let's perform the calculations:
Interest = $32,500 × 0.075 × (180/365)
Discount = $32,500 × 0.08
Proceeds = $32,500 - Discount
By substituting the values in the formulas and performing the calculations, we can find the proceeds to the bank.