Ray's New Practical Arithmetic · Arts. 190–191 · Unit 17: Interest
91. Compound interest and annual interest
Goal: Your child computes compound interest year by year, and understands annual interest (interest charged on unpaid yearly interest).
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 237 defines Compound Interest (Art. 190). Page 238 works an example and gives the rule, with problems on pages 238–239. Page 239 defines Annual Interest (Art. 191), and page 240 works it with a rule and problems, which run onto page 241.
The lesson, step by step
Warm-up
Ask: If your $100 earns $10 this year, and next year you earn 10% on $110, how much do you earn the second year?
Compound interest
Find the compound interest of $300 for 3 yr., at 6%.
$300 → $318 → $337.08 → $357.3048. Subtract $300: $57.30.
The rule: find the amount for the first year and make it the next year's principal, and so on; then
From the last amount subtract the given principal; the remainder will be the compound interest.
Annual interest
Annual Interest is interest on the principal, and on each annual interest after it is due.
Ray's example: a $400 note at 6%, payable annually, unpaid for 4 yr. 8 mo. 24 da. Interest on the principal: $113.60. Each yearly $24 also earns interest for the time it stayed unpaid. Those times add to 8 yr. 11 mo. 6 da., which gives $12.864. Amount due: $526.46.
Guided practice
Do these two together:
Of $500, for 3 years.
(Compound, at 6%.)
No interest having been paid, find the amount due in 3 yr. on a note for $800, with interest at 8%, payable annually.
Independent practice and check
Your child works some compound interest problems on pages 238–239 and some annual interest problems on pages 240–241. 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.
Mental-math wrap-up
Aloud: $100 at 10% compound for 2 years (amount $121); simple interest for the same (amount $120).
Tip
Old customs note: the book explains that compound interest was made legal by taking up the old note each year and giving a new one for the principal plus the interest. Annual interest could be collected when the note said "with interest payable annually".