Ray's New Higher Arithmetic · Arts. 257–259 · Unit 16: Percentage: Applications without Time (continued)
69. Premium and discount: Cases II to IV
Goal: Your student finds the rate of premium or discount, the par value from the premium or discount, and the par value from the market value.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Case II (find the rate), Case III (find the face from the discount or premium) and Case IV (find the par value from the market value), each with a formula, notes and examples. Answers are printed.
The lesson, step by step
Warm-up
Quick review from Case I: What does 50 shares ($100 each) cost at 3% premium? ($5150.)
Case II: find the rate
Read the heading:
Given the face and the discount or premium, to find the rate.
The rate is the premium or discount divided by the par value. Work:
Received $4.60 for an uncurrent $5 note: what was the rate of discount?
Discount = $.40; $.40 ÷ $5 = .08 = 8%.
Case III: find the face
Read:
Given the discount or premium and the rate, to find the face.
Divide the premium or discount by the rate. A small example of our own: a discount of 2% came to $40. The face was $40 ÷ .02 = $2000.
The book's Case III examples ask for a number of shares. Find the face first, then divide by the price of one share.
Case IV: from market value to par
Read the heading:
Given the market value and the rate, to find the par value.
Par value = market value ÷ (1 + rate of premium), or ÷ (1 − rate of discount). Work:
Invested $1591 in stocks, at 26% discount: how many shares ($50 each) did I buy?
$1591 ÷ .74 = $2150 of par value; $2150 ÷ $50 = 43 shares.
An important warning
Read the book's note:
Bear in mind that the rate of premium or discount, and the rate of profit or loss, are entirely different things
SayPremium and discount are measured on the face. Profit and loss are measured on what you paid.
Independent practice
Your student works a few examples from each case. Have them write the case number beside each problem before starting.
Check and wrap-up
Compare with the printed answers. Ask: Which number is the base in all four cases? (The par value.)
Afterwards
Two sittings work well: Cases II and III, then Case IV.
Tip
In every case, write down first whether the stock or draft is above par or below par. Most mistakes come from adding a discount or subtracting a premium.