A local bank lends $12,000 using a 150-day 9% simple interest note that was signed on May 18. The bank later sells the note at a discount of 14% on July 5. Find (a) the discount, (b) the proceeds, and (c) the amount of money the bank gains or loses.
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To find the answers to this question, we need to calculate the discount, proceeds, and gain/loss of the bank using the given information. Let's break it down step by step.
Step 1: Calculate the interest payable.
Interest is calculated using the formula: Interest = Principal x Rate x Time.
In this case, the principal (P) is $12,000, the rate (R) is 9% (expressed as 0.09), and the time (T) is 150 days.
Interest = $12,000 x 0.09 x (150/365) [Converting days to years by dividing by 365]
= $438.36 (approximately)
Step 2: Calculate the maturity value.
Maturity value is calculated by adding the principal amount with interest.
Maturity Value = Principal + Interest
= $12,000 + $438.36
= $12,438.36
Step 3: Calculate the discount.
Discount is the difference between the maturity value and the selling price.
Discount = Maturity Value x Discount Rate
= $12,438.36 x 0.14 [Converting the discount rate to decimal]
= $1,733.17 (approximately)
Step 4: Calculate the proceeds.
Proceeds are the selling price of the note after applying the discount.
Proceeds = Maturity Value - Discount
= $12,438.36 - $1,733.17
= $10,705.19 (approximately)
Step 5: Calculate the gain/loss.
The gain/loss is the difference between the maturity value and the proceeds.
Gain/Loss = Maturity Value - Proceeds
= $12,438.36 - $10,705.19
= $1,733.17 (approximately)
Now let's summarize the answers:
(a) The discount is approximately $1,733.17.
(b) The proceeds are approximately $10,705.19.
(c) The bank gains or loses approximately $1,733.17. In this case, the bank loses this amount as the note was sold at a discount.