Investing · Lesson Plan
Annuities and Perpetuities
An annuity is a series of equal payments made on a regular schedule — mortgage payments, college-fund deposits, and loan payments are all annuities; a payment stream that continues forever is a perpetuity. This lesson builds from the future-value formula FV = P(1 + r)n to the future value of an annuity, with worked examples students can follow step by step.
For Teachers
Lesson at a glance
- Topic
- Investing
- Grade Level
- Grades 11–12 / College
- Resource Type
- Lesson + Worksheet
- Estimated Time
- 45–60 minutes
- Format
- Lesson + worked examples
- Materials
- Printable lesson, worked examples, calculator
What Students Learn
Learning objectives
- Define an annuity and a perpetuity
- Recognize annuities in everyday life
- Apply the future-value formula FV = P(1 + r)^n
- Calculate the future value of an annuity
- Distinguish a fixed future value from an annuity’s future value
Materials
What you’ll need
- Printed lesson with worked examples (one per student)
- Calculator
- Scratch paper
- Whiteboard
Key Terms
Vocabulary
- Annuity
- A series of equal payments or receipts made on a regular basis.
- Perpetuity
- An annuity whose payments continue indefinitely.
- Future value (FV)
- What an amount invested today will be worth later.
- Principal
- The starting amount invested or borrowed.
- Interest rate
- The rate of return earned each period.
- Term
- One payment period in the series.
For Teachers
Lesson plan
Estimated time: one 45–60 minute class period.
Lesson sequence
- Define (10 min). Annuities vs. perpetuities, with real examples (mortgage, college fund, scholarship endowment).
- Future value (15 min). Work through FV = P(1 + r)^n with the two worked examples.
- Future value of an annuity (15 min). Introduce FVa and work an annuity example.
- Practice (10 min). Students compute FV and FVa for new figures.
Assessment
Assess the worked practice problems for correct use of the future-value formulas.
Discussion
Discussion questions
- What is an annuity, and where do you see annuities in everyday life?
- How is a perpetuity different from an ordinary annuity?
- What does the future-value formula tell you?
- Why does the future value of an annuity use a different formula?
- Why did insurance companies begin offering annuities?
Printable Lesson & Worked Examples
Annuities and Perpetuities — Lesson & Worked Examples
A printable financial-math lesson on annuities and perpetuities, building from future value to the future value of an annuity with worked examples.
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