Ray's New Higher Arithmetic · Arts. 310–312 · Unit 19: Percentage with Time: True and Bank Discount
86. True discount and present worth
Goal: Your student finds the present worth of a debt due later, and its true discount.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Section III, True Discount: discount for cash, present worth, true discount, the difference from a merchant's discount, a worked problem and rule, and examples. Answers are printed.
The lesson, step by step
Warm-up
Ask: Would you rather have $100 today or $100 a year from now? Why?
The idea
Read:
Present Worth is that sum of money which, at a given rate of interest, will amount to the same as the debt at its maturity.
True Discount, then, is the difference between the present worth and the whole debt.
Not a shop discount
Read:
Discount on a debt must be carefully distinguished from Commercial Discount, which is simply a deduction from the regular price or value of an article
Say"20% off" in a store is commercial discount. True discount is about time and interest.
Work the book's example
Find the present worth and discount of $5101.75, due in 1 yr. 9 mo. 19 da., at 6%.
$1 grows to about $1.10817 in that time. $5101.75 ÷ 1.10817 = $4603.775, the present worth. The discount is $497.975.
The rule
Read:
Divide the debt by the amount of $1 for the given time and rate; the quotient is the present worth.
SayThis is Case V of interest again: the debt is the amount, and the present worth is the principal.
Practice and check
Your student works the examples, such as:
Find the true discount on a debt for $5034.15 due in 3 yr. 5 mo. 20 da., without grace, at 7%.
Check the printed answers.
Wrap-up
Ask: Is the present worth of a debt more or less than the debt? (Less, unless the debt is due now.)