Math 1 · Unit 8 · Lesson 2

Compound Interest, Interest on Interest

Simple interest adds, compound interest multiplies. With compound interest each year's interest goes into the account and earns interest too, so the dollars added grow every year: not a line. The shortcut is the distributive property: adding 5% is multiplying by 1.05, because keeping all of it is times 1 and the interest is 0.05 more. After t years the balance is P times (1 + r) to the t, the exponential family from Unit 7 with P as the starting value and 1 + r as the growth factor.

About 45 minutes The factor is 1 plus the rate

The big idea

Simple interest adds, compound interest multiplies. With compound interest, each year's interest joins the account and earns interest the next year, so the dollars added grow every year and the average rate of change keeps rising: not a line. Adding r to a balance is multiplying it by 1 + r, because keeping all of the money is multiplying by 1 and the interest is r more, which is the distributive property at work. So each year multiplies by the growth factor 1 + r, and after t years the balance is A = P(1 + r) to the t. That is y = a times b to the x from Unit 7: P is the starting value and 1 + r is the growth factor, a constant ratio. Reading an expression backward, the number in front is the first deposit and the factor splits into 1 plus the rate. The balance can never be 0, because a positive amount times a positive factor stays positive.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Interest on interestLesson 1 was the line: simple interest pays on the principal only, so it adds the same dollars every year. 3The shortcut: multiply by 1 plus the rateWorking out 5% and adding it on, year after year, is slow. 4Reading an expression, and moving P and rNow read an expression somebody else wrote. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the interest-on-interest table, the multiply-by-1-plus-r shortcut, the formula next to y = a · b^x, reading an expression, and a worked example with calculator keys. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Simple Interest, the Line in MoneySimple interest adds. Next lesson: Compounding More OftenThe yearly rate, split into pieces and paid more often. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.F-IF.8b (interpret growth and decay rates), NC.M1.F-LE.5 (interpret the parameters in context), NC.M1.A-SSE.1b (read a group of parts as one quantity), NC.M1.F-IF.6 (average rate of change).