#### Bank Discount

The sum charged by a *bank * for cashing a note or time draft is called *bank discount*. This discount is the simple interest, paid in advance, for the number of days the note has to run. Wholesale business houses usually sell goods on *time * and take notes from the retailers in payment. These notes are not often for a longer period than *three months*. Some are placed in the banks for collection, others are *discounted*. When a note is discounted at a bank the payee *indorses * it, making it payable to the bank. Both maker and payee are then responsible to the bank for its payment. If the note is drawing interest the discount is reckoned on and deducted from the amount due at maturity. Most notes discounted at banks do not draw interest. The *time * in bank discount is always the number of days from the date of discounting to the date of maturity.

Example: A note of $250, dated July 7, payable in 60 days, is discounted July 7 at 6%; find the proceeds.

Explanation: This note is due in 63 days, or September 8. The accurate interest of $250 for 63 days at 6% is $2.59. The proceeds, then, will be $250-$2.59, or $247.41.

The *Present Worth * of a note or debt is a sum, which, if put at interest, will amount to that debt in the given time.

The *True Discount * is the difference between the debt at maturity and its present worth.

Remember:

1. *To allow three days of grace, if the debt discounted is a note.*

2. *To add the interest due at maturity to the principal, before discounting, if the note bears interest.*

Examples: Case I.—Note not bearing interest.

What is the present worth and true discount on a note of $200, if paid 6 months before due, the discount being 6%.

Solution: Amount of $1 for 6 months at 6% = $1.03. If $1.03 = amount of $1, $200 is the amount of as many dollars as 200 ⁄1.03 , or $194.17+.

$194.17 is the present worth. $200 - $194.17 = $5.83 true discount.

The following rule can be deduced from the foregoing solution :—

Rule: 1. *To find the present worth, divide the debt by the amount of $1 for the given time.*

2. *To find the true discount, subtract the present worth from the debt.*

Case II.—Note bearing interest.

What is the present worth of a note of $300, bearing 6% interest, due in 2 years 4 months, if money is worth 10%.

Solution: Interest on $300 for 2 years 4 months at 6% = $42.

$300 + $42 = $342. Amount due at maturity.

Amount of $1 for 2 years 4 months at 10% = $1.23 1 ⁄3.

If $1.23 1 ⁄3 = amount of $1, then $3.42 is the amount of $342 1.23 1 ⁄3 , or $277.29.

$277.29 = present worth.