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Lecture notes Business mathematics (BMD115D)
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Notes and in depth explanation of how to deal with SIMPLE INTEREST
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CHAPTER 12: SIMPLE INTEREST12.1 INTRODUCTION
What is Interest
Cost involved in borrowing money or the reward received when lending money is
referred to as interest. That is, income received from capital that has been invested
or money paid for the use of borrowed money.
Inflation and Interest Rate
• Price levels of goods and services will rise if the supply of money in the
economy increases more quickly than the availability of goods and services
(economic outputs).
• Inflation is the term used to define continued increases in the general level of
process in the economy. Inflation is also used to define the decline in the
purchasing power of money that occurs when the demand for goods and
services is greater than the supply of goods and services.
Inflation
• Inflation is usually accompanied by increased interest rates. As price levels
increase, investors anticipate the loss in the buying power of their money and
require more interest to compensate for the reduced value of their investment
when the principal is repaid.
• As inflation continues over time the rand value of our money buys less goods
and services. This leads to increasing pressure on interest rates and wage
levels.
Interest
There are two methods of calculating interest on income received and or money paid
out. These are:
• Simple interest
• Compound interest
Chapter 12 and Chapter 13 looks at the application of both methods.
, The following are basic principles and notations used in all interest calculations.
• P – Present value – amount at the beginning of the transaction
• Term – total number of periods for which the principle is used
– t – simple interest
– n – compound interest
• F – Future value – amount at the end of the transaction
Interest received or paid is based on four factors:
• The amount of money lent or invested, P
• The rate of interest, R or i
• The duration of the debt of investment, T or n
When applying interest formulae to a problem, the element to be found must
be identified first.
12.2 SIMPLE INTEREST
This is the interest calculated based on the original principal during the entire period
at the stated interest rate.
Formulae for Simple Interest
• Simple Interest: I
𝐼 =𝑃 ×𝑟 ×𝑡 key formula
• Maturity or accumulated value: S
𝑆 = 𝑃(1 + 𝑟𝑡) key formula
• Principal invested or borrowed: P
𝑆
𝑃 = 1+𝑟𝑡 key formula
Where:
o P = Principal or present value
o R = Rate of interest, expressed as a fraction
o T = Time, in years
o I = Total simple interest
o S = Future value
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