Ray's New Practical Arithmetic · Arts. 198–199 · Unit 18: Discount
95. True discount and present worth
Goal: Your child finds the present worth and true discount of a debt due later, and compares it with bank discount.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 256 defines True Discount (Art. 198) and gives Art. 199. Page 257 works two examples, page 258 gives the rule and problems, and page 259 has more problems. 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
The present worth of a debt is the sum which, put at interest now, would grow to the debt by the time it is due.
The true discount is the difference between the present worth and the amount of the note.
Notes, debts, and running accounts are discounted by True Discount.
Work the book's example
Find the present worth and discount, at 6%, of a note of $430.50, due in 2 yr. 5 mo. 18 da.
The amount of $1 for that time is $1.148. Present worth = $430.50 ÷ 1.148 = $375. Discount = $55.50.
1. Find the amount of $1 for the given time at the given per cent. 2. By this divide the amount of the note; this is the present worth.
Guided practice
Do these together:
Find the present worth and discount, at 6%, of a note of $224, due in 2 yr.
A merchant bought a bill of goods amounting to $775, on 4 months' credit: if money is worth 10% to him, what might he pay for the goods in cash?
Bank discount vs. true discount
Problem 12 on page 259 compares the two on $535 for one year at 7%. Bank discount takes interest on the whole $535. True discount takes interest only on the present worth, so it is a little smaller. Work it together.
Independent practice and check
Your child works a selection from pages 258–259. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.