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. I do not know what formula to use.

Answer 1

We will find the proceeds to the bank by following these steps:

1. Calculate the simple interest using the formula: Interest = Principal × Rate × Time
2. Find the maturity value, which is the sum of the loan amount and the interest.
3. Calculate the time, in days, that the bank held the note before selling it.
4. Calculate the discount on the note using the formula: Discount = Maturity Value × Discount Rate × Time Held by Bank
5. Find the proceeds to the bank by subtracting the discount from the maturity value.

Step 1: Calculate the simple interest
Interest = $32,500 × 7.5% × 180/360
Interest = $32,500 × 0.075 × 0.5
Interest = $1,218.75

Step 2: Find the maturity value
Maturity Value = $32,500 + $1,218.75
Maturity Value = $33,718.75

Step 3: Calculate the time held by the bank
The bank held the note from January 7 to March 2. The total number of days between these two dates is 54 days.

Step 4: Calculate the discount
Discount = Maturity Value × Discount Rate × Time Held by Bank
Discount = $33,718.75 × 8% × 54/360
Discount = $33,718.75 × 0.08 × 0.15
Discount = $404.63

Step 5: Find the proceeds to the bank
Proceeds to the Bank = Maturity Value - Discount
Proceeds to the Bank = $33,718.75 - $404.63
Proceeds to the Bank = $33,314.12

So, the proceeds to the bank are $33,314.12.