Bernie borrowed 8,000.00 for 180 days from lion bank. The bank discounted the note at 5% A) what proceeds does Bernie Receive? B) Calculate the effective rate to the nearest hundredth percent.
A) "Discounting the note" means that they paid him 5% less ($7600).
B) If they expect full payment in 180 days, with no additional interest, then the effective annualized interest rate is
$400/$7600 x 360/180 = 10.53%
I thought that it was 8000 x .05 x .5000 and that would have been 200
To find the proceeds Bernie receives, we need to calculate the discount amount that the bank deducts from the original loan amount.
A) The discount is equal to the interest charged by the bank for the duration of the loan. To calculate the discount, we use the formula:
Discount = Principal Amount × Interest Rate × Time
Since Bernie borrowed $8,000.00 and the bank discounted the note at 5% for 180 days (or 0.5 years), we can substitute these values into the formula:
Discount = $8,000.00 × 0.05 × 0.5
Discount = $200.00
Therefore, Bernie receives $8,000.00 - $200.00 = $7,800.00 in proceeds.
B) To calculate the effective rate, we need to determine the total interest paid relative to the proceeds received.
Effective Rate = (Total Interest / Proceeds) × 100
Since Bernie receives $7,800.00 in proceeds and the discount charged by the bank is $200.00, the total interest paid is $200.00.
Effective Rate = (200 / 7800) × 100
Effective Rate = 0.025641 × 100
Effective Rate = 2.5641%
Hence, the effective interest rate is approximately 2.56% to the nearest hundredth percent.