Ray's New Higher Arithmetic · Arts. 319–320 · Unit 20: Percentage with Time: Exchange
90. Exchange and domestic exchange
Goal: Your student explains how a debt in a distant city was paid with a bill of exchange, and finds the cost of a domestic draft.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Section V, Exchange: definitions (exchange, bill of exchange, domestic and foreign exchange, set of exchange, rate, course and par of exchange), a sample foreign bill, then domestic exchange with a worked problem, a rule and examples. Most answers are printed.
The lesson, step by step
Warm-up
Ask: In 1880, how could a merchant in St. Louis pay a debt in New York without mailing gold coins?
The idea
Read:
Exchange is the method of paying a debt in a distant place by the transfer of a credit.
it avoids the danger and expense of sending the money itself.
A Bill of Exchange is a written order on a person or company in a distant place for the payment of money.
Domestic Exchange treats of drafts payable in the country where they are made.
Rate of exchange
Read:
The Rate of Exchange is a rate per cent of the face of the draft.
SayA draft on New York might sell at ½% premium in Chicago if many people wanted to send money to New York.
Work the book's example
What will a 30 day draft on New Orleans for $7216.85 cost, at ⅜% discount, interest 6%?
At ⅜% discount, each $1 of draft costs $.99625. The buyer also waits 33 days for the money, so take off the bank discount of $1 for 33 days, $.0055. Each $1 costs $.99075. $7216.85 × .99075 = $7150.09.
Guided practice
Do one sight draft (no waiting, so no bank discount) and one time draft from the page together.
Independent practice
Your student works more examples. Include Example 12, which has no printed answer:
If a 45 day draft for $5500 costs $5538.50, find the rate of exchange.
Wrap-up
Ask: Why does a time draft cost less than a sight draft for the same face? (The buyer waits for the money, so interest is taken off.)
Answers to the book's problems
Ex. 12: each $1 of the draft cost $5538.50 ÷ $5500 = $1.007. Add back the bank discount of $1 for 48 days (45 + 3 grace) at 6%, $.008: the rate is $1.015, or 1½% premium. (Ex. 13 and 14 print their answers in the problem: ¾% discount and 2% premium; both check.)
Worked out for this site from the scan. If a number in your copy differs, trust the book.