math class 678 4-in-1 skill sheets
Compound Interest and Rewriting Rates, Algebra 1 4-in-1 Skill Sheet (HSA.SSE.B.3c)
HSA.SSE.B.3c Algebra 1 Unit 9: Exponential Functions

Compound Interest and Rewriting Rates

I can rewrite an annual growth expression to reveal its monthly rate.

View on TPT Back to Unit 9

The problem this sheet solves

Students write the monthly factor for 6% a year as 1.005. Twelve of those compound to 1.0616778, an annual rate of 6.17% rather than the 6% the problem stated, because each month's interest then earns interest. The true monthly factor is BELOW a twelfth, which is the surprise, and the difference is invisible without carrying enough decimal places. This sheet rewrites the rate with a twelfth root and shows why that is exact where dividing is not, and the equivalence is proved symbolically rather than checked at a couple of sample values, since a numerical check cannot separate equal from very close. That distinction is precisely what students are being asked to trust.

The key rule

To find a monthly rate, take the 12th ROOT of the annual factor and multiply the exponent by 12. Dividing the rate by 12 gives too much, because interest compounds.

12th root, not a twelfth.

Watch out

The mistake: For 6% a year a student writes the monthly factor as 1 + 0.06 ÷ 12 = 1.005.

The fix: The monthly factor is 1.061/12 = 1.0048676. Twelve months of 1.005 compound to 1.0616778, an annual rate of 6.17% — more than the 6% the problem gave, because each month's interest then earns interest.

What is included

  • Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
  • Practice page — six problems, building from foundational to multi-step
  • Apply page — a word problem, a reasoning prompt, and an error-analysis task
  • Assess — a half-page exit ticket, two to a sheet, with a score box
  • Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
  • Ink-saver edition of all 7 pages
  • 14-slide teacher deck (PowerPoint) with presenter notes on every slide

Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.