1. Simple vs Compound Interest
Albert Einstein once said, "Compound interest is the eighth wonder of the
world. He who understands it, earns it. He who doesn't, pays it."
Now, in other words, compounding is a very powerful tool in finance,
and it's even more noticeable when you have a longer time period.
This chart demonstrates how an initial $100 can grow in value by simple
interest in orange and by compound interest in blue.
As you can see in the chart, the effect of compounding grows as
the number of years increase. We can actually build this model in our Excel
template, and this will allow us to explore what happens with different
interest rates. So if we want to replicate the chart that we just
saw, comparing a simple 5% interest rate with a compounding 5%
interest rate, we need to go back to our demo sheet in our
workbook and scroll down to the simple interest versus compound interest
section, which starts in row 52. Now we've got a chart there already, and
that's going to reference our inputs or results from columns E and G. So
you don't have to worry about anything. The chart will populate
if you do the simple interest in column E and the compound interest
in column G. We're gonna start with a principle of 100.
We're going to have a 5% interest rate,
and we are going to do it for 50 years. How much do
we have after 50 years? So going down to our table that we
need to complete. Now our periods is gonna start at zero and go
all the way up to 50 years. So we could type it,
we could do a little formula. I like to use the sequence function
for this. So I start typing sequence until I see it,
hit tab, and you can see that we've got four inputs here.
The number of rows is going to be the number of years,
50 years plus one because we're going to start at zero,
so we actually need 51 rows. Now we are going to do this
one column wide 'cause we just want them all in column C. We
want to start at zero as I mentioned, and we want to go
up by one year each time, so step is one. So there's my
sequence function there. And when you hit Enter, you'll see that that sequence
function automatically generates a sequence from zero up to 50,
which is brilliant. So our simple interest, we're going to start at term
zero, with 100, right? And you can see the chart starting to populate.
How much do we have each year in simple interest? Well, we're going
to earn 5% simple interest each year. So I'm going to absolutely reference
that, and I'm going to multiply that by the principal amount because that's
how simple interest works. And I'm going to add that to the amount
that we had the year before. All right, so there's my formula for
calculating simple interest each year. And so now what I can do is
hold the Shift+Arrow down all the way down to year 50
and I can just come back up here and Ctrl+D, and you can
see after 50 years we've got $350. So let's just scroll back up
to the top, and you can see the chart has populated for us.
You can see the simple interest going up in a linear fashion.
We are earning $5 interest each year. What about compound interest?
Well, again, we're going to start with 100.
So we can reference that 100 there. Now you can calculate the annual
interest rate by taking the 5%, and again, we'll absolutely reference that
by pressing F4, but we're gonna multiply that by our starting amount each
year, which is found the year before. And to that, I'm going to
add the amount in the year before. So there's our formula for compound
interest. And again, I'll do the same thing. Hold Shift+Arrow down,
all the way down to 50 years, and then Ctrl+D, and you can
see that we have a lot more with compound interest. We've got 1,146.74.
And if we scroll back up to our chart, you can see that
chart has populated. And very visually, you can see how powerful compound
interest is. We have the same starting amount, we have the same interest
rate, we have the same term, but because for compound interest,
interest is compounding annually, we end up with a lot more after 50
years. And actually because we've got this nice model, you could change
the interest rate and the difference is even more pronounced if you have
a higher interest rate. So let's say 8%,
8%, hit tab and you can see how much more interest we'll have
under compound interest than simple interest. Compounding interest is very,
very powerful. Well done on getting to the end of the first chapter
on simple and compound interest. I really hope that you worked alongside
me when we went through the Excel demonstrations. Now you may have noticed
in the Excel workbook there's another sheet called extra exercises. And
here I've provided you with a number of compound and simple interest questions
so you can practice developing your skills. In the chapters coming up in
the rest of the course, you'll also be downloading different Excel workbooks,
and there are extra exercises in all of them to help you practice
the skills that you'll be developing in the rest of this course.
2. Let's practice!