MA.912.FL.3.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.NSO.1.1 
• MA.912.AR.2.1
• MA.912.AR.2.2
• MA.912.AR.2.5

Terms from the K-12 Glossary

• Simple Interest

Vertical Alignment

Previous Benchmarks

• MA.7.AR.3.1

Next Benchmarks

• MA.912.FL.3.3
• MA.912.FL.3.4

Purpose and Instructional Strategies

• In this benchmark, students will be introduced to the concepts of simple and compound interest and will solve real-world problems that feature them. 
• Instruction compares the differences between simple and compound interest. 
  • The simple interest formula ($I$ = $p$$r$$t$) calculates only the interest earned over time. Each year’s interest is calculated from the initial principal, not the total value of the investment of that point in time. 
  • The simple interest amount formula ($A$ = $P$(1 + $r$$t$)) calculates the total value of an investment over time. 
  • The compound interest formula ($A$ = $P$(1 +  $\frac{\text{<math><mi>r</mi></math>}}{\text{<math><mi>n</mi></math>}}$)^$n$$t$) also calculates the total value of an investment over time. Each month/year’s interest is calculated from the total value of the investment of that point in time. 
• Compound interest problems presented for this benchmark may require students to generate equivalent expressions to identify and interpret certain parts of the context. 
  • For example, Jason deposits $850 in an account that earns an annual interest rate of 4.8%. The interest is compounded monthly and Jason wants to determine the total amount interest he will earn in one year. With the given information, derive that the value of the account is equal to 850 (1 + $\frac{\text{0.048}}{\text{12}}$)^12$t$. The expression can be 12 rewritten as 850[(1.004)¹²]^$t$ leading to 850(1.049)^$t$ to find that the total amount interest in a year would be approximately 4.9% of his initial investment.

Common Misconceptions or Errors

• Some problems related to this standard may ask students for the interest earned over a period of time while others may ask for the account balance or total value of the investment over a period of time. Some students may miss this distinction and may always calculate total interest for simple interest problems and total value for compound interest problems. In these cases, point students back to the working of the problem and help them assess the reasonableness of their answers (MTR.6.1) in context.

Strategies to Support Tiered Instruction

• Teacher provides a highlighter to identify if a question is asking for the interest or the total amount. 
• Instruction provides a graphic organizer to identify the important information in a problem. 
  • For example, given a simple interest problem, students could complete the following table. 
    
    
    

• Instruction includes the opportunity to distinguish between an expression and an equation. These should be captured in a math journal. 
  • For example, when generating equivalent expressions, place an equal sign in between the expressions and label each expression and the equation.

Instructional Tasks

• Felipe signs up for a new airline credit card that has a 24% annual interest rate. If he doesn’t pay his monthly statements, interest on his balance would compound daily. If Felipe never pays his statements for a full year, what would be the actual percentage rate he would pay the credit card company? 

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