1. Title Slide
Did you answer this poll question right before this lesson? If so,
which one did you choose? We can actually use Excel to figure out
the best option, but first, you'll need to download another Excel workbook,
which we'll use in this chapter. And this workbook is called Effective and
Nominal Interest Rates Template. So pause the video now if you still needto download this workbook and press play when you're ready. So here we
are in our effective and nominal interest rates template workbook, and I've
gone to the demo sheet and we want to answer the question,
which bank, bank A or B is the best bank to deposit out
$1000 worth? So let's start with Bank A. We are going to deposit $1000.
They are offering us a 10% interest rate and they're saying that they're
going to pay us interest on a quarterly basis, so the frequency is
four. Now how many times a year do we get our interest payment?
Well, we take our one year and we divide it by the compounding
frequency of four. Let me just do that again. One divided by four.
And so we get paid interest every quarter of a year.
So let's complete the table starting by with zero,
at four time today. And then we're going to add one quarter of
year to this each time. So we're going to start with the time
period before and we're going to add one quarter of a year,
which we will absolutely reference and we can just fill that down,
and then, we see our four compounding periods. Now,
our total value, well we're starting with a $1000, so times zero, we've
got a 1000, so we can just pull that in there.
How much interest do we have or will we earn? Well, we're going to
earn interest based on the starting amount here and it's going to be
10%, but we are going to get quarter of that every...
For every three months. And again, we'll absolutely reference that and just
tad to go along. And we can see that we're gonna get $25
at the end of the first three month period, the end of the
first quarter. So our total value will be our starting amount plus the interest
there. So now, we've got this formula that we can see that we
calculate the quarterly interest and we are adding it to the total value.
So now, if I just highlight those two columns, E and F and
then Ctrl+D to fill down, you can see that at the end of
the year, bank A is going to pay us 1,103.89. What about bank
B who's paying interest on a monthly basis? While again, we're going to
have a $1000, to start with, the nominal interest is still 10%,
but now the compounding frequency is 12, and the compounding period is gonna
be one year divided by the frequency. And so one month is 0.08 of
a year. So our time and year is starting at zero for today.
And now we're going to add 0.8 of a year... 0.08 of a year,
I should say each time period. So, we can now fill this down
and hit Ctrl+D and there's our one year broken into monthly periods. We're
going to start at time zero with our present value of a 1000. And
our interest is going to be our nominal interest rate,
absolutely reference divided by the compounding frequency absolutely reference.
And we're going to multiply that by the amount that we have at
the start of the period, which we just get here,
1000 in cell L13. And we're not going to absolutely reference that because
B want that to be relatively referenced. Hit tab to go along.
We see in the first month we earn 8.33 worth of interest,
which we can add to the total amount that we have 1000. So
at the end of the first month, we'll have 1008.33. Now because we've
got the formulas in there, we can just highlight the columns K and L
and Ctrl+D to fill down. You can see that bank B
is actually going to give us 1104.71 at the end of the year,
which is a little bit more than bank A due to the higher
frequency of the compounding. So we can think about this a little bit
more by scrolling down and completing this table. Right? So to complete
this table we can see the effect of increasing the compounding frequency.
So if we have a present value of a 1000, and our nominal industry is
10%, as before, what will our present value and our future values be? So
our present value is always going to be a thousand, right? So I'm
gonna absolutely reference that by pressing F4 and I can just fill that
down. Now what about our compounding frequency? Well, annual compounding
means the compounding frequency is just going to be one.
Semi annual, our compounding frequency will be two. Quarterly, as in bank
A, the compounding frequency will be four. Monthly compounding means we
have a compounding frequency of 12, weekly is 52. And if we assume
365 days in the year, our daily compounding means our frequency is 365.
So what will our future values be? Well, our future value is going to be
the present value times open bracket one plus the nominal interest rate,
and we can absolutely reference that divided by the compounding frequency,
and we won't absolutely reference that, we want that to remain as a
relative reference, all raised to the number of compounding periods if again.
And so, we can see that if we have annual compounding,
we'll have 1100 at the end of the year. If we have semi annual compounding,
I can just fill down with Ctrl+D. We'll have 1102.5 Now we know
what we'll have with quarterly compounding because that's what bank A paid
us. And again, if we just Ctrl+D to fill down, there we see
the same result that we see in the top of the screen,
1103.81. Monthly compounding is bank B, and we can see that we get
the same result, 1104.81. And if we increase the compounding periods,
we can see that our future value increases and increases. So here's the
table that we've just constructed back in the Excel workbook where the nominal
interest rate was 10%. And here is that key takeaway that I really
want you to remember. Increasing the compounding frequency accelerates the
growth of the investments future value because interest is calculated and
added to the principle more frequently leading to a higher accumulated amount
over time.
2. Let's practice!