Unit 8
Principles of Compound Interest

This unit presents the properties of compound interest and related mathematical calculations. Compound interest is of fundamental importance in the world of finance. Commonly applied to long-term debts or financial obligations, compound interest involves the periodic conversion of simple interest to principal. As a result of this conversion, interest is calculated on interest, and the compounding process can lead to some very dramatic results. For example, $1,000 invested at 8% simple interest would amount to only $5,000 in 50 years. On the other hand, $1,000 invested at 8% would amount to $46,901.61 in 50 years, if it were invested in such a way that the interest earned each year is converted to principal, on which further interest is calculated in each succeeding year. That is, compounding yields an additional $41,901.61 in 50 years.

In this unit, we discuss definitions of terms, the formulas for basic operations, the concepts of “present value” and “equivalent values,” fractional or incomplete compounding periods, and using the compound interest formula to find values other than the compound amount. The principles you learned in Unit 7, such as time lines and equivalent values, are similar to the ones in this unit. The difference is that the principles in this unit use compound interest.

Objectives

After completing this unit, you should be able to perform the following tasks.

1. Define the terms “compound amount,” “compound interest,” “equivalent value,” and “focal date,” and calculate each value.
2. Set up an “equation of value” to compute the equivalent values of old and new obligations on a focal date.
3. Do problems involving “present value” and “future value,” and “discounting” for loans or investments charging or earning compound interest.

Note: You will now need a business financial calculator, which incorporates preprogrammed financial functions to make the chore of doing calculations easier, especially in the financial math calculations. The text shows the key strokes etc. to solve problems using the Texas Instruments BA II Plus financial calculator. This is an excellent calculator for financial Math and Statistical Analysis. Using this calculator will be a convenience for you in this course. If you do not have a financial calculator then we recommend you purchase the Texas Instruments BA II Plus. However, there are many financial calculators on the market and you may already have one. If you already have a financial calculator, then ensure you have the instruction manual that came with the calculator as you will need it to learn the key strokes to do the financial calculations. You will be allowed to use the calculator throughout the course and in your examinations. Calculators are wonderful tools that help us, but ensure you understand the mathematical concepts and formulas you are applying. Do not just memorize keystrokes.