## Lecture 2: What is Simple Interest?

Let’s have a look at what simple interest actually is. Firstly, a recap of some background stuff about interest. So remember that in any financial transaction there are two parties: an investor who is lending money to someone and a debtor who is borrowing money from the investor.

So the debtor must pay back the money originally borrowed but also a fee charged for the use of the money. So the debtor needs to pay back money to the investor. Now that money like we said not only includes the money that was borrowed but also a fee for the use of that money. So the terms that we use when we talk about that are our principal and/or present value, or interest. That is the money that gets paid back to the investor.

Now an interest transaction can be described by the interest rate, which is a fraction of the amount borrowed over time. Now let’s look at interest and interest rate and what it looks like in regards to simple interest. Firstly, let’s have a look at what simple interest is.

Simple interest: Interest that is worked out on the principal (money borrowed) for the entire term of the loan at the stated annual interest rate and is, therefore, due at the end. So you pay it at the end of the loan period.

There is a formula that we are going to use for simple interest and it looks like this:
I = Prt

Now, what does this formula mean?
I = simple interest (in Rand)
P = principal/total amount borrowed/present value (in Rand)
R = simple interest rate (as a decimal for calculations)
T = time/term (in years)

With simple interest, we’re always going to be working in years. You’ll see just now, even if you’ve been given days, you need to convert it to a portion of the year those days are.

Let’s break this formula down a bit. When you have letters written next to each other like this, remember that it is actually times. So, P x R x T.

If you think back to the example we did with Jan and Sarah in the previous video, we looked at the R10 000 with Jan, and we added 10% of the R10 000. So, the R is like that 10% and the T was 1 year, and the P was the 10%. Remember that we times it together, so this formula gives you the actual interest that was charged on a loan during a period of time. So, that’s is our formula for interest.

Please note: This formula is on your formula sheet, so take it out and write Simple Interest next to it, so that by the time you get to the end of the whole course, you’ve got a formula sheet that is fully labelled and you know where everything is.

Now, let’s look at a note about our term. Remember that I said that a term had to be in years. What happens when they give it to you in months or days? You need to convert that back to years.

For example, if you are given months then take your number of months and divide it by 12 because there are 12 months in a year. This will give you the portion of years. If you are struggling to get the idea, then do it with something simple like 6 months divided by 12. This will give you half a year. If you simplify that fraction, remember when we simplify we divide the numerator and the denominator by the same amount, so we can divide them both by 6. So 6 divided by 6 is 1, 12 divided by 6 is 2. That’s half; 6 months is half a year. So do you see how this allows you to get a portion of the year?

With days, we are always going to take it as 365 days in a year. So we will take the number of days, and we divide it by 365.

With weeks, we are going to take 52 weeks in a year. So it will be our number of weeks divided by 52.

Here is a screenshot with all the calculations: Now let’s look at an example. If I tell you that we are borrowing money for 9 months, then we are going to have 9 out of 12. That’s the portion of the year, so that’s how many years – nine-twelfths of a year – and that’s what your T will be. You’re more than welcome to simplify that fraction – divide 9 by 3 and 12 by 3 and that gives you ¾ of a year.

We’ve looked at how to determine the interest, and what happens if we are given days or months or weeks instead of a full year.

Now, how do I calculate the sum accumulated? The amount you have to pay back at the end.

Let’s break this down and look at what formula to use for this.

For sum accumulated we use the letter S.

S = principal + interest – Remember, we’ve got the original (the principal), and we need to pay back that and the interest.

So let’s use our notation here:
S = P + I

In the previous slide, we saw that we had a formula for working out I, so let’s put that in place of I.
S = P + Prt

Now we’re going to do something mathematical, so think back to school when you did factorising, and you had to take out the highest common factor. This P is common to both of these terms, the things that are separated by a +. So we take out the common P, and we’re going to have 1 plus R times T.
S = P (1 + rt)
So this is now our formula that we’re going to use for determining the sum accumulated.
This is another formula that’s on your formula sheet, so label it Simple Interest again on your formula sheet.

Just a reminder - when you have letters written next to each other like this, remember that it is actually times. So S = P x (1 + r x t). If you think of BODMAS, when we’re working this out, we would have to do whatever’s inside those brackets first before we times. If we’re breaking it down, which we’re going to do later, then we use BODMAS backwards.

Remember that:
S = sum accumulated (in Rand)
(Future value)

Here is a screenshot with all the calculations: In the videos to come, we are going to look at some examples of how we use simple interest.
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