# MA.912.FL.3.3

Solve real-world problems involving present value and future value of money
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Financial Literacy
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Exponent
• Exponential function
• Linear function

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In Algebra I, students explored and compared investments involving simple and compound interest and solved real world problems related to those types of investments. In Math for Data and Financial Literacy, students use their new knowledge of these interest formulas to solve real-world problems involving the present value or future value of investments.
• 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.

• 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

Instructional Item 1
• 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?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1700600: GEAR Up 1 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
1700610: GEAR Up 2 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
1700620: GEAR Up 3 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
1700630: GEAR Up 4 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
2102305: Economics and Personal Finance Honors (Specifically in versions: 2023 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessment

College Costs:

Students are asked to transform an exponential expression so that the rate of change corresponds to a different time interval.

Type: Formative Assessment

## MFAS Formative Assessments

College Costs:

Students are asked to transform an exponential expression so that the rate of change corresponds to a different time interval.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.