Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Define an annuity and its different types.
• Calculate the future value (FV) of an annuity.
• Calculate the present value (PV) of an annuity.
• Apply these calculations to real-world scenarios like saving, loans, and retirement.

Lesson summary

Annuities and long-term planning are fundamental concepts in personal finance, particularly crucial in the South African context. Understanding these concepts allows learners to make informed decisions about their financial future, including saving for retirement, investing, and managing debt. In South Africa, where economic inequalities and fluctuating markets are prevalent, financial literacy empowers individuals to navigate these challenges and build a secure future. This week's focus is on understanding the basics of annuities, differentiating between various annuity types, and exploring their application in long-term financial planning.

Lesson notes

What is an Annuity? An annuity is a series of regular payments made or received over a specified period of time. It's a contract between you and a financial institution, where you either pay a lump sum or a series of payments, and in return, you receive regular payments in the future. Annuities are commonly used for retirement planning and other long-term financial goals.

Types of Annuities: Ordinary Annuity: Payments are made at the end of each period. This is the most common type of annuity. For example, monthly loan payments or regular savings into a retirement account.

Annuity Due: Payments are made at the beginning of each period. For example, rent payments.

Deferred Annuity: Payments begin at some future date. For example, a retirement annuity where you contribute now but receive payments after retirement.

Future Value of an Ordinary Annuity: The future value (FV) of an ordinary annuity is the total value of the annuity at the end of the payment period, including all payments and accumulated interest.

Formula: FV = P * [((1 + i)^n - 1) / i] Where: FV = Future Value P = Periodic Payment (the amount of each regular payment) i = Interest rate per period (expressed as a decimal) n = Number of periods Present Value of an Ordinary Annuity: The present value (PV) of an ordinary annuity is the current worth of a stream of future payments, discounted at a specified interest rate. It represents the lump sum amount you would need to invest today to generate the same stream of payments in the future.

Formula: PV = P * [(1 - (1 + i)^-n) / i] Where: PV = Present Value P = Periodic Payment (the amount of each regular payment) i = Interest rate per period (expressed as a decimal) n = Number of periods

Worked example

Example 1: Future Value of an Ordinary Annuity (Saving for a Car)

Sipho wants to save for a car. He plans to deposit R500 per month into a savings account that pays 6% interest per year, compounded monthly. He will make these deposits for 3 years. What will be the future value of his savings?

P = R500

i = 6% per year / 12 months = 0.06 / 12 = 0.005 per month

n = 3 years 12 months = 36 months

FV = 500 * [((1 + 0.005)^36 - 1) / 0.005]

FV = 500 * [((1.005)^36 - 1) / 0.005]

FV = 500 * [(1.19668 - 1) / 0.005]

FV = 500 * [0.19668 / 0.005]

FV = 500 * 39.336

FV = R19,668

Therefore, the future value of Sipho's savings after 3 years will be R19,668.