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Transcript: Introduction to Compound Interest
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BYU-Idaho Online Learning

Video Transcript

Introduction to Compound Interest

[One speaker]

Speaker: Welcome to the introduction to compound interest. But let’s start out by discussing what simple interest is and comparing it to what compound interest is, and I’ll do that with a series of pictures.

[Throughout the video pictures of different blocks appear to represent principal amounts and interest amounts related to the principal. Each time period has a start and end to the period which has a blue ‘P’ block to represent the principal.]

So, in the first period, or the first time amount that we calculate the interest on, and depending on the loan, that time period could be a month or it could be a year or it could be something else, so I’m just going to call each of these a period of time. So, in the first period of simple interest, we start out with our initial principal amount, [points to ‘P’ block under “start period 2”] and then at the end of that period [points to ‘P’ block and small ‘I’ block next to it under “end period 1”] we have the principal plus the little amount of interest, that’s a percentage of the principal, added to it. Then, at the beginning of the second period, [similar blocks appear for the second period under “start period 2” and “end period 2” except there are two ‘I’ blocks to represent two interest amounts] we start again with the same amount of principal, and at the end of the period we add another little piece of interest that’s the same size as the interest from the first period. So now we have two identical sizes of interest added to our principal. At the end of the third period, [blocks for the third period appear. There are now three ‘I’ blocks] again we’re talking about simple interest. We start again with our original amount, and this time, at the end of the period, we add another little chunk of interest that’s the same size as the interest that was calculated in the second period and the first period. So, at the end of the third period, we have three little chunks of interest that are all the same size that have been added to our original amount.

Now compound interest, in its first period, is exactly the same. [the first period for compound interest looks identical to the first period for simple interest] We start with our principal amount, and then at the end of that period, we calculate the interest on the principal as a percentage of the principal and add it to the principal. So we have the principal plus a little bit of interest. It changes though when we come to the second period. [the blocks for the second period of compound interest appear. [under “start period 2” the ‘P’ block has the ‘I’ block inside of it and the block is bigger than all the previous ‘P’ blocks which have been equal in size] In the second period, we actually take the amount that we had at the end of period one, the principal plus the interest, which is now a bigger chunk of money and we calculate the interest on 8that entire amount, the principal plus the interest from the first period. So at the end of period two, [under “end period 2” the ‘P’ block with the ‘I’ block inside is there along with another ‘I’ block that is slightly bigger than all the previous ‘I’ blocks which have been equal in size] the interest that was calculated, which is represented by this green square, is a little bit bigger than the interest that was calculated at the end of period one, because this interest at the end of period two is calculated on the principal plus the interest from period one. So it’s being calculated on a slightly bigger amount. We can see this even more obviously in period three. [blocks for period three appear. At the start the ‘P’ block has the two previous ‘I’ blocks in it and it is a little bigger, and at the end the there is another ‘I’ block that is slightly bigger than all the previous ones next to the ‘P’ block that has two ‘I’ blocks inside of it] At the beginning of period three, we’re now starting with the principal, the original amount, plus the interest from period one, plus the interest from period two as our starting amount. This is a much bigger square than we started with in period one, and is bigger than what we started with in period two. Now, at the end of period three, our interest is calculated on this much bigger amount. So the interest at the end of period three is a larger amount then was calculated at the end of period two which was also bigger than the interest calculated at the end of period one. So over time, compounding interest can yield significantly more interest than simple interest, because every compounding period calculates more interest than the period before it.

[End of video.]