# 1.0 Introduction

**Chapter Learning Objectives**

By the end of the chapter you should be able to:

- Differentiate between the concept of compound interest and simple interest
- Define terms related to compound interest
- Calculate future value for compound interest
- Calculate present value for compound interest
- Calculate equivalent payments that replace another payment or a set of payments
- Calculate the interest rate of a loan or investment
- Calculate the number of compounding periods
- Calculate the term of a loan or investment
- Calculate effective interest rates
- Calculate equivalent interest rates

Do you dream of owning a home? What about a car or a home theatre system? Big purchases such as these require long-term financial planning. Compound interest means that you will pay substantially more money for your purchases or earn more money on investments than you would with simple interest.

In the previous chapter, you learned about simple interest. In simple interest, all interest is based solely on the original principal amount of the transaction, and the interest is converted to principal at the end of the transaction. But in compound interest, the interest also earns interest. **Compound interest** involves interest being periodically converted to principal throughout the transaction, with the result that the interest itself also accumulates interest. Compound interest is used for most transactions lasting at least one year.

But how significant is the interest when it compounds? Consider the following scenarios:

- A home theatre system with the big-screen TV, Blu-Ray player, stereo surround sound, and more can retail for [latex]\$5,000[/latex]. Did you know that if you put that amount on the retail store’s [latex]18\%[/latex] interest credit card and pay it off monthly for three years, you will pay over [latex]\$1,500[/latex] of compound interest?
- You want to purchase a new car that retails for [latex]\$35,000[/latex]. Unless you have that amount of cash on hand, you will join the ranks of other Canadians who take out car loans to purchase their new car. If you take six years to pay-off this loan at an interest rate of [latex]4.5\%[/latex] compounded monthly, you would have to make monthly payments of [latex]\$555.59[/latex] and pay over [latex]\$5,000[/latex] in interest on the loan.
- To purchase a house that is listed for [latex]\$600,000[/latex], you take out a [latex]25[/latex] year mortgage at [latex]6\%[/latex] compounded semi-annually. Over the course of the [latex]25[/latex] years, you will pay over [latex]\$550,000[/latex] in interest on the mortgage, which almost doubles the original cost of the house.

And it is not any different for businesses. Whether they are local companies or multinational conglomerates they must invest and borrow at compound interest rates in their attempt to achieve long-term financial strategies. Some examples of these business activities include the following:

- Borrowing [latex]\$480,000[/latex] to open a new restaurant.
- Spending [latex]\$1,000,000[/latex] on a fleet of rigs and semi-trailers for product distribution.
- Constructing new production plants or warehouses costing [latex]\$10,000,000[/latex] or more.

The money for these types of transactions does not appear out of thin air. It must be borrowed or taken from savings, and either approach involves compound interest. Throughout the rest of this textbook, you will study compound interest as it relates to three distinct but interconnected concepts:

- Calculating interest on a single amount (called a lump-sum amount or single payment).
- Calculating interest on a series of regular, equal payments, called annuities.
- Specialized applications including amortization, mortgages, bonds, sinking funds, net present value, and internal rates of return.

“Chapter 9″ from Business Math: A Step-by-Step Handbook Abridged by Sanja Krajisnik; Carol Leppinen; and Jelena Loncar-Vinesis licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

“Chapter 9 Introduction” from Business Math: A Step-by-Step Handbook (2021B)by J. Olivier and Lyryx Learning Inc.through aCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.