1. Title Slide
This table shows how the language used is really important to understand
whether we're dealing with a nominal or effective interest rate. Where no
compounding period is stated, it's an effective rate with compounding assumed
to be equal to the stated time period.
5% per year is an effect of 5%
compounded annually. 1% per month is an effect of 1%
per month compounded monthly. When a compounding period is given without
study if the rate is nominal or effective, it's assumed to be a
nominal rate. 8% per year compounded semi annually is a nominal 8%
compounded on a semi annual basis. The effective rate is higher than 8%
per year. When an interest rate is stated as an effective rate,
it's a bit clearer that this is indeed an effective interest rate.
Effect of 5% per compounded monthly means the nominal rate is lower than
5% per year. Compound interest is a very powerful tool. This is the
same message I gave you at the end of chapter one when comparing
simple and compound interest. But it's so powerful, I actually want to revisit
it again, this time using the language of nominal and effective interest
rates. Have a look at this table. What we have here is the
same nominal interest rate of 5%, but compounded at increasing frequencies.
Could you look at what the effect of rate would be for monthly
compounding? In practice, banks can't compound any more frequently than
daily, although in theory, you could have more compounding periods within
a year then 365. Now, let's see if we can replicate this table
backing our Excel workbook. So I've scrolled down to the last section on
our demos sheet of our effective and nominal interest rate template workbook.
And again, just to finish off, I want to recap some of the
things that we've talking about in this chapter.
The nominal rate is 5%, well, it starts with a nominal rate of 5%, and
I want to compare that to the effective rate for different compounding frequencies
annually, semi annually, quarterly, monthly and daily. Let's say that we've
got an initial deposit of 100,000, now, what will the nominal rate be
with different compounding frequencies? Where the nominal rate is always
5% because the nominal rate is the interest rate before the effect of
any compounding. So regardless of the number of compounding period, our
nominal rate will always be 5%. What's the effective rate? Well,
let's practice converting that nominal rate into the effective rate using
that formula that we see and read. The effective rate equals bracket one
plus the nominal rate divided by the frequency
or raised to the frequency minus one. And if we fill that down,
we can see that as the compounding frequency increases, the effective rate
also increases, now that's really important because our effective rate is
increasing because the compounding frequencies is increasing. Our balance
at the end of the year is going to be higher.
So our balance at the end of the year is going to be
the 100 that we have at the start of the year. And I'll
just absolutely reference that, and I'm going to multiply that by
bracket one plus the effective interest rate. So we can see that if
we had annual compounding, we have 105,000 at the end of the year,
but if I just hold it there and Ctrl+D to fill down,
you can see that as we increase the frequency of our compounding,
the effective rate is also increasing and therefore our balance at the end
of the year is getting larger and larger.
2. Let's practice!