Math 1 · Unit 8 · Lesson 4

Which Account Wins?

Put a simple interest account and a compound interest account in a race. Kevin's $100 earns $5 every month, a line. Joseph's $100 earns 3% every month, an exponential. Kevin leads for more than two and a half years, then Joseph passes him for good. A quantity that grows by multiplying always passes one that grows by adding, sooner or later, so the better account depends on how long you leave the money.

About 45 minutes Multiplying passes adding, sooner or later

The big idea

Lines add, exponentials multiply, and when you race them the exponential wins in the end. Kevin's account adds $5 every month and Joseph's multiplies by 1.03 every month. Kevin is ahead after two years, $220.00 to $203.28, but Joseph's monthly gain keeps growing while Kevin's stays at $5, so Joseph takes the lead at about 33 months and never gives it back. The same thing happens with City Bank and National Bank: the simple interest account with the higher rate leads for 10 years, and the compound account wins after that. So which account is better depends on how long you leave the money, and the longer you wait, the more compound interest wins. To compare accounts given in different ways, put them in the same form, and find the crossing from a table or a graph, the way you read an intersection in Unit 6.

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 2Kevin and Joseph: $5 a month, or 3% a month?Two friends each invest $100. 3Two banks, two forms: City Bank and National BankReal choices come in different forms: one bank gives you a sentence, another a formula, another a table. 4Sort the money storiesA fixed number of dollars each step adds: linear. A percent each step multiplies: exponential. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with Kevin and Joseph, the crossing at 33 months, City Bank and National Bank, and the big idea that multiplying passes adding. 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: Compounding More OftenRate per period and number of periods. Next lesson: When Money Shrinks, and Using the ModelsThe same form going down, interest working against you, and what-if questions. 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-LE.3 (exponential growth eventually exceeds linear), NC.M1.F-IF.9 (compare functions represented in different ways), NC.M1.F-LE.1 (linear or exponential from how it changes over equal steps).