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Stepping Stones: Introducing Simple Annuities
Stepping Stones: Introducing Simple Annuities
Welcome to the world of annuities! In this lesson, we'll lay the groundwork for understanding these powerful financial tools. We'll begin by exploring simple annuities, a fundamental type of annuity where payments are made at the end of each period.
Get ready to:
Define key terms related to simple and general annuities, building a strong vocabulary.
Illustrate simple and general annuities, visualizing their structure and payment schedules.
Distinguish between simple and general annuities, understanding their key differences.
Calculate the future and present values of simple annuities, mastering essential formulas.
Compute the periodic payment of a simple annuity, applying your knowledge to practical scenarios.
By the end of this lesson, you'll have a solid grasp of simple annuities, setting the stage for exploring more complex annuity types in the lessons to come. Let's get started!
Activity: Investing for the Future
Activity: Investing for the Future
Scenario: Imagine you're saving for a down payment on a house. You decide to deposit ₱10,000 every six months into an investment account that earns 6% interest compounded semi-annually. The payments are made at the beginning of each six-month period.
How much will you have saved after 5 years?
Analysis: Understanding the Formula
Analysis: Understanding the Formula
Can you discuss other real-world examples of general annuities due, such as lease payments, insurance premiums, and certain types of savings plans on the comment box below?
This lesson introduces the concept of simple annuities, a fundamental building block in financial mathematics. Let's dive in!
Formulas for Simple Ordinary Annuities
Formulas for Simple Ordinary Annuities
Future Value (F)
Present Value (P)
Periodic Payment (R):
To achieve a desired future value (F)
To amortized a present value (P)
Where:
F = Future Value
P = Present Value
R = Regular Payment
i = Interest rate per period
n = Number of periods
Examples
Examples
1. Simple vs. General Annuity:
Scenario: Payments at the end of each month, interest compounded quarterly.
Type: General Annuity (payment interval and compounding period differ).
Scenario: Deposit of P5,500 every three months, interest at 5.6% compounded quarterly.
Type: Simple Annuity (payment and compounding intervals align).
2. Ordinary Annuity vs. Annuity Due:
Scenario: Monthly mortgage payment of P35,148.05 at the end of each month.
Type: Ordinary Annuity (payments at the end of periods).
Scenario: Rent of P7,000 due at the beginning of each month.
Type: Annuity Due (payments at the beginning of periods).
3. Future Value Calculation:
Problem: Mrs. Remoto saves P3,000 monthly in a fund earning 9% compounded monthly. What's the future value after 6 months?
Solution:
R = P3,000
i = 9%/12 = 0.09/12 = 0.0075 (monthly interest rate)
n = 6 months
F = R * [(1 + i)^n - 1] / i = 3000 * [(1 + 0.0075)^6 - 1] / 0.0075 ≈ P18,340.89
4. Present Value Calculation:
Problem: Rose wants to withdraw P36,000 every 3 months for 20 years, starting 3 months after retirement, with a 12% annual interest rate compounded quarterly. How much should she have at retirement?
Solution:
R = P36,000
i = 12%/4 = 0.12/4 = 0.03 (quarterly interest rate)
n = 20 years * 4 quarters/year = 80 quarters
P = R * [1 - (1 + i)^-n] / i = 36000 * [1 - (1 + 0.03)^-80] / 0.03 ≈ P1,087,22
Want to master steady income streams? Here's a video lesson to understand more about simple annuities and their future and present values!
Ready to test your knowledge of simple annuities? This assessment will evaluate your understanding of key terms, your ability to illustrate and differentiate between annuity types, and your skill in calculating future and present values of simple annuities.
Application
Application
Instruction: Use online resources, critical thinking, and the provided information to answer the following questions. Justify your answers with explanations and calculations. Upload your documents on this google drive link: Module 2 Lesson 1 Activity Outputs
(Note: Make sure your file name will be your Section-Year-Surname-Given_Name-Module#-Lesson#-Output#, for example: [GAS11-DelaCruz-Juan-Module1-Lesson1-Output1]. Wrong file name will subject to score deduction.)
Scenario: Imagine you've won a lottery that offers you two payment options:
Scenario: Imagine you've won a lottery that offers you two payment options:
Option A: Receive P10,000 at the end of each year for the next 5 years.
Option B: Receive P40,000 in a lump sum today.
Guiding Questions:
Understanding the Basics:
What is an annuity?
Can you identify which lottery option represents an annuity?
What factors might influence your decision between a lump sum and an annuity?
Simple vs. General Annuities:
Assuming the lottery prize money is invested at a fixed interest rate, would this scenario be considered a simple annuity or a general annuity? Why?
How often would interest be compounded in this case?
Time Value of Money:
Is P10,000 received today worth the same as P10,000 received a year from now? Why or why not?
What concept helps us understand the changing value of money over time?
Calculating Future Value:
If you choose Option A and invest each yearly payment at 5% interest, how much money will you have at the end of 5 years?
What formula can you use to calculate this?
Calculating Present Value:
How much is Option A (receiving P10,000 annually for 5 years) worth today if we consider a 5% discount rate?
What formula can you use to calculate this?
Making Informed Decisions:
Based on your calculations, which lottery option seems more financially beneficial? Why?
What other factors (besides pure monetary value) might you consider when making your decision?
Extension Activities:
Research real-life examples of simple annuities (e.g., regular savings plans, certain types of loans).
Create and solve your own word problems involving simple annuities.
Discuss the advantages and disadvantages of simple annuities compared to other investment options.
Mastered simple annuities? Let's dive into the world of general annuities in Lesson 2!
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