A retailers has an account for #20000 from a manufacturer who gives two months' credit, but offers a cash discount of 5% for prompt payment. The retailer borrows #20000 from his bank at 9% per annum for two months and pays promptly to secure the cash discount. How much does he gain by this transaction?
Well, let's crunch some numbers and find out how much our retailer gains from this transaction.
First, let's calculate the interest on the loan from the bank. The interest amount for two months at an annual rate of 9% would be 9/12 * 20000 = #1500.
Second, let's calculate the cash discount. The cash discount is 5% of the account amount, which is 5/100 * 20000 = #1000.
Now, let's subtract the interest paid on the loan from the cash discount received: #1000 - #1500 = -#500.
Uh-oh! It appears that our retailer actually ends up losing #500 by taking the cash discount and borrowing money from the bank. So, in this case, caution is the best currency!
To determine how much the retailer gains by taking advantage of the cash discount, we need to calculate the costs of both options: borrowing from the bank and paying without the discount, or borrowing from the bank and paying with the discount.
Option 1: Borrowing from the bank and paying without the discount:
The retailer borrows #20000 from the bank at an interest rate of 9% per annum. Since the payment is due in two months, we need to calculate the amount of interest for this period.
Interest = Principal * Rate * Time
= #20000 * (9% / 12 months) * 2 months
= #300
The retailer would have to pay #300 as interest for the two-month loan.
Option 2: Borrowing from the bank and paying with the discount:
In this scenario, the retailer borrows #20000 from the bank but pays promptly to secure a cash discount of 5%.
Discount = #20000 * 5%
= #1000
The retailer gains #1000 as a cash discount by paying promptly.
To calculate the net gain from this transaction, we subtract the interest paid from the cash discount gained:
Net Gain = Cash Discount - Interest
= #1000 - #300
= #700
Therefore, the retailer gains #700 by taking advantage of the cash discount and choosing to borrow from the bank at a lower interest rate.