MA.912.FL.3.3

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.NSO.1.1
• MA.912.NSO.1.6
• MA.912.NSO.1.7 
• MA.912.AR.2.5  
• MA.912.AR.5.7 
• MA.912.AR.10.1
• MA.912.AR.10.2

Terms from the K-12 Glossary

• Exponent 
• Exponential function 
• Linear function

Vertical Alignment

Previous Benchmarks

• MA.912.FL.3.4

Next Benchmarks

Purpose and Instructional Strategies

• The present value of investments is the sum of money that must be invested to achieve a specific future goal. 
  • To calculate the present value of an investment, students should solve their interest formula for the variable P. 
  • For single deposit investments, this leads to: 
    
    
    

• For periodic investments, this leads to: 
  
  
  

• The future value of investments is the dollar amount that will accumulate over a given time-period when that sum is invested. Most of students’ work with interest formulas in MA.912.FL.3.1 and MA.912.FL.3.2 has focused on exploring future values of investments. 
  • For single deposit investments students use  .
  • For periodic investments students use .

• Given the complexity of the formulas used in this benchmark, be sure to calculate one example by hand and by technology to confirm any formulas entered into spreadsheet technology are calculating correctly. 
• When using spreadsheet technology for analysis, multiple problems can develop as students create and enter formulas for calculations. Write sample formula entries for compound interest, = 2000 ∗ (1 + 0.04/12)^(12 ∗ 5), on the board for them to emulate to help prevent this. Note that many programs require a ∗ symbol to denote multiplication. Placing two variable (or cells) side by side may generate a REF error. 
• While using spreadsheet technology, as students learn to reference other cells in their formulas, there will be cases where they want a single cell’s value, like the principle of an investment, to remain in the formula as they copy it to multiple rows of a table. To achieve this, students should type a “$” symbol in front of the part of the cell name they want to remain static. 
  • For example, when copying formulas that reference cell A1 across multiple rows/columns, using $A1 will allow the rows to change, using A$1 will allow the columns to change, and using $A$1 will maintain that specific cell in every row/column.

Common Misconceptions or Errors

• The formula for periodic investments is complex. Students should solve portions of the formula over several steps to ensure accurate calculations. Recording these steps in writing can help identify errors for miscalculations.

Instructional Tasks

• Idris wants to save $20,000 over the next 6 years to buy her first car. She researches investment options and finds three investments to consider. Investment A offers 1.3% interest compounded monthly. Investment B offers 1.9% interest compounded semiannually. Investment C offers 2.1% interest compounded annually. For each investment, how much would Idris need to deposit each year to meet her goal? Which investment is the better deal?

Instructional Items

• Pasha invests $6,000 each year into a mutual fund that averages 11.6% interest, compounded annually. Assuming the average interest rate doesn’t change, how many years will it take for her reach $1,000,000? How many years will it take for her to reach $2,000,000?

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