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.
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.
To find the proceeds to the bank, we need to calculate the unpaid balance of the loan on March 2 and then subtract the discount amount.
First, let's calculate the interest charged on the loan for 180 days:
Interest = Principal x Rate x Time
Interest = $32,500 x 7.5% x (180/365)
Next, calculate the unpaid balance on March 2 using simple interest:
Unpaid Balance = Principal + Interest
Now that we have the unpaid balance, we can find the discount amount. The discount is calculated as a percentage of the unpaid balance:
Discount = Unpaid Balance x Discount Rate
Finally, the proceeds to the bank is calculated by subtracting the discount amount from the unpaid balance:
Proceeds to the Bank = Unpaid Balance - Discount
Let's calculate it step-by-step:
Step 1: Calculate the interest charged on the loan for 180 days
Interest = $32,500 x 7.5% x (180/365)
Interest = $32,500 x 0.075 x 0.4932
Interest = $1,235.25
Step 2: Calculate the unpaid balance on March 2 using simple interest
Unpaid Balance = Principal + Interest
Unpaid Balance = $32,500 + $1,235.25
Unpaid Balance = $33,735.25
Step 3: Calculate the discount amount
Discount = Unpaid Balance x Discount Rate
Discount = $33,735.25 x 8%
Discount = $2,698.82
Step 4: Calculate the proceeds to the bank
Proceeds to the Bank = Unpaid Balance - Discount
Proceeds to the Bank = $33,735.25 - $2,698.82
Proceeds to the Bank ≈ $31,036.43
Therefore, the proceeds to the bank is approximately $31,036.43.
To find the proceeds to the bank, we need to calculate two things: the interest accrued by Sheila Spinney, and the discount applied when the bank sold the note.
First, let's calculate the interest accrued by Sheila Spinney using the formula for simple interest:
Interest = Principal × Rate × Time
Here,
Principal = $32,500
Rate = 7.5% (which can be written as 0.075)
Time = 180 days
Plugging the values into the formula, we get:
Interest = $32,500 × 0.075 × (180/365)
Interest = $32,500 × 0.075 × 0.49315
Interest ≈ $1,215.52 (rounded to the nearest cent)
Now, let's calculate the discount applied by the bank. Discount is expressed as a percentage of the face value of the note. In this case, the discount is 8% (or 0.08) of the face value.
Discount = Discount Rate × Face Value
Face Value is the original principal borrowed, which is $32,500.
Discount = 0.08 × $32,500
Discount = $2,600
The proceeds to the bank is the difference between the face value of the note and the discount:
Proceeds = Face Value - Discount
Proceeds = $32,500 - $2,600
Proceeds = $29,900
Therefore, the proceeds to the bank are $29,900.