Simple and Compound Interest

1. Learning Objectives • I know the difference between simple and compound interest • I am able to apply the principle of compounding to other fields • I know the formula for calculating simple and compound interest • I understand the principles of simple and compound interest • I understand the principles of depreciation • I can apply these principles to unseen problems Simple and Compound Interest

2. Percentage A percentage is a proportion of a number. It is represented as a number out of one hundred. The word percent can be separated into per- and –cent. Per- means over, cent means 100. Percent therefore means over 100. This circle is cut into seven pieces. The pink pieces represent two pieces out of seven i.e. 2/7 i.e. 28.6% The green piece represent one pieces out of seven i.e. 1/7 i.e. 14.3% The yellow pieces represent four pieces out of seven i.e. 4/7 i.e. 57.1%

3. Scenario: You want to buy a car. The car costs R 50 000. You don’t have the money so you go to the bank and you ask the bank to borrow you the money. The bank guy then says: “Okay, we’ll give you the money but you have to pay it back over 5 years with a simple interest rate of 10% per year.” You say: “What does this actually mean?” He says: “ This means that you will pay back the R50 000 over 5 years and pay 10% of the loan added on to that.” You say: “I still don’t understand. ” He says: “10% of R50 000 is R5 000. You would need to pay R10 000 every year or 5 years in order for you to have paid the full amount back in 5 years. With the interest of R5 000 per year you will pay R15 000 per year. This brings the total repayment to R75 000. ” You say: “Oh okay, now I understand!”

4. Terms you must understand Beware(Watch yourself): I use the words Principal and Principle in this topic. Principal refers to the starting amount. Principle refers to what we are doing when we calculate interest. Principal Amount This is the R50 000 in the scenario. The actual amount of money you borrowed. Interest Rate This is how we denote each of these concepts This is the 10% in the scenario. The percentage of the principal amount that will be added on to the principal amount. Period Present Value This is the representation of time period. This is the amount of money you owe or have paid at the present time. P i n PV

5. Interest Linear relationships are relationships that grow in a straight line. This means that interest ,in this case, grows by the same amount. Exponential relationships are relationships that grow in an exponential way. This means that interest, in this case, grows by a percentage of the previous amount. • Interest is the added amount that you need to pay over the amount that you actually borrowed. • Interest is calculated in two different ways: • Simple interest • Compound interest • Interest is an example of things that grow or increase over time. • Simple interest is a relationship of linear growth. • Compound interest is a relationship of exponential growth.

6. Simple and Compound Interest Compound interest model: exponential relationship Simple Interest Compound Interest • With simple interest, you add the same amount each year of the given period of repayment. • So in our example, we will take 10% of the principal amount(R50 000) which is R5 000. • We will add this R5 000 to whatever repayment we make each year for the 5 years. • The situation in the scenario presented in the previous slides represents simple interest. • With compound interest, you add a percentage of interest of the amount in the previous term of repayment. • So in our example, we will begin by taking 10% of the principal amount which is R5 000. • Then we will add this on to the principal amount to get R55 000. Then we take 10% of this amount(R5 500) and add it on to the R55 000. Etc… • The following table will illustrate. Let’s assume a repayment amount of R 10 000 per year 70 000 65 000 60 000 55 000 50 000 rand Simple interest model: linear relationship + + + + + x 10% x 10% x 10% x 10% Principal amount 0 1 2 x 10% n With compound interest the money or repayment increases by an increasing amount each year. Between year 0 and 1 it’s R5 000, between year 1 and 2 it’s R 5 500. With simple interest the money or repayment increases by the same amount(R5 000) each year. At this point, the linear relationship and the exponential relationship are equal.

7. Simple and Compound Interest Work out the PV of the example using both simple and compound interest. Use the formulas with the 1 in them and then take the 1 out and compare your findings. Formulas Simple Interest Compound Interest As you can see, trying to calculate simple interest and compound interest from tables and graphs can be tedious and time-consuming and BORING!!! mathematicians found formulas that make our lives much much easier. PV= P(1+i)n PV= P(1+ni) Present Value equals the principal value multiplied by (1 plus the period we want times interest rate). Present Value equals the principal value multiplied by (1 plus the interestrate to the power if the period we are interested in evaluating). Thankfully, The reason why we use 1+i and 1+ni instead of just i and ni is because i is a fraction(because it is a percentage), and if you multiply a number by a fraction, it decreases the quantity of a number. So adding 1 makes sure that the number does not decrease to its proportion, but has it’s proportion added on to it.

8. STOP Take a breathe, and click after you are sure you understand the slides preceding this one.

9. Depreciation • Depreciation works in the inverse of the principle of interest. • Interest describes the increase from the starting point • Depreciation describes the decrease from the starting point • With simple depreciation, we calculate the gradual(linear) decrease from the starting point • With compounded depreciation, we calculate the exponential decrease from th starting point

10. Scenario: • After finding out that you will have to pay R30 000 extra on the car you wanted, you decide to “review” your decision. • One of the things you consider in your “review” is; if the car is worth R50 000 now, how much will it be worth when you are done paying for it after 5 years? • You then conduct an investigation. In this you find out the following: • Your car will depreciate in value. • It will depreciate by 10% per annum from the time you first drive it.

11. Simple and Compound Depreciation Simple depreciation Compound depreciation • With simple depreciation, you calculate 10% of the value on the principal amount • Each year you deduct the same amount from the total • With compounded depreciation, you calculate 10% of the value of the principal amount • You then subtract this from your principal amount • The following year you calculate 10% of the present value you have and deduct that from the total. Etc. - - - - 10% 10% 10% 10%

12. Depreciation Simple depreciation Compounded depreciation PV=P(1-ni) PV=P(1-i)n Compounded depreciation doesn’t really make much sense so, simple depreciation is used for the calculation of depreciation.

13. Quick Quiz • Instructions: • Write on a clean piece of paper • Keep the paper clean and neat until Saturday • Answer all questions • What is the principle of interest • What is simple interest • What is compound interest • What are the formulas for compound and simple interest • In your opinion, which is the better type of interest principle for businesses • What is the difference between simple and compounded interest relationships • What is the difference between simple and compounded depreciation relationships

14. Task • Conduct an investigation of how much interest would be on a car and what the repayments would be • Conduct an investigation of how much the same car would be worth in 72 months with the current market depreciation rate • Put a teaspoon of yeast in a plastic bag and leave it on your window seal for the week, make sure the bag is closed