Ray's New Higher Arithmetic · Arts. 316–318 · Unit 19: Percentage with Time: True and Bank Discount
89. Bank discount: face of a note, and rates of interest
Goal: Your student finds what face a note needs to give wanted proceeds, and compares a discount rate with the true rate of interest it means.
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 face from the proceeds), Case III (the rate of interest a discount rate really gives) and Case IV (the discount rate that gives a wanted interest rate), each with a worked problem, a rule and examples.
The lesson, step by step
Warm-up
Ask: If a bank takes $10 off the front of a $100 loan for a year, are you really paying 10% interest? (You only got $90, so it's more: $10 on $90 is 11 1/9%.)
Case II
Read:
For what sum must a 60 da. note be drawn, to yield $1000, when discounted, at 6% per annum?
The discount on $1 for 63 days is $.0105, so $1 of face gives $.9895. $1000 ÷ .9895 = $1010.61.
Try together:
The face of a 60 da. note, which, discounted at 6% per annum, will yield $800.
Case III
Read:
Given the rate of bank discount, to find the corresponding rate of interest.
The book's example: a 60-day note at 2% a month. On $100 the discount for 63 days is $4.20, so the borrower gets $95.80. The interest of $95.80 at 1% for 63 days is $.16765. $4.20 ÷ $.16765 = about 25%.
A lesson in the remark
Read:
Hence, the profit of the discounter is greater proportionally on long notes than on short ones, at the same rate.
Case IV
Read the rule:
Find the interest and the amount of $100 or $1 for the given time.
Divide the interest by the interest of the amount at 1% for the given time; the quotient is the corresponding rate of discount.
Practice
Your student works a few examples from each case. The Case IV answers are hard to read in the scan; use the answers below to check.
Wrap-up
Ask: Is a 6% discount rate the same as 6% interest? (No: it is a little more than 6% interest.)
Answers to the book's problems
Case IV (worked at a 360-day year, with 3 days of grace on the 30, 60 and 90 day notes; rounded): 1) 30 da. notes yielding 10, 15, 20%: discount at 9.91%, 14.80%, 19.64%. 2) 60 da. notes yielding 6, 8, 10%: 5.94%, 7.89%, 9.83%. 3) 90 da. notes yielding 1, 2, 4% a month (12, 24, 48% a year): 11.64%, 22.60%, 42.70% a year. 4) 1 yr. without grace yielding 5, 6, 7, 8, 9, 10%: 4.76%, 5.66%, 6.54%, 7.41%, 8.26%, 9.09%.
Worked out for this site from the scan. If a number in your copy differs, trust the book.