1. Title Slide
So you can see that if we know the compounding frequency for any
nominal rate, we can find an effective rate, but also for any effective
rate, we can find the nominal rate. On the left hand side,
we can see that a nominal rate of 10%
compounding quarterly gives an effective rate of 10.38%. This can be checked
by going back the other way. On the right hand side,
we're starting with an annual effective rate of 10.38%. This gives a nominal
rate of 10%, getting us back to where we started.
Let's get back into Excel and make sure that we can get the
same results as we see here. The formulas can be a little tricky
to remember, so I've made sure that these are also written in the
Excel workbook. So here we are picking up from where we were when
we last visited our Excel workbook for the chapter, when we completed the
table to calculate the effective rate for different compounding frequencies.
Below that we've got some space to practice converting a nominal rate into
an effective rate, first of all, and then an effective rate into a
nominal rate. So let's put some inputs in and the loan amount is 10,000,
the nominal interest rate is 10%, and we want to convert that to
an effective rate if the compounding frequency is a four and we've got
a one year period. So the key things that we need to calculate the
effective rate from a nominal rate is the nominal rate and the compounding
frequency, so we can pick that up there.
So down below cell D152 and D153, we've got the formula to calculate the
effective rate if we know the nominal rate. We can say it's equals
bracket one plus the nominal rate, which is 10%, which you've just picked
up here, divided by the frequency four, all raised
to the frequency of four, minus one, and we can see that the
effective rate is 10.38. And you can see that in the table above,
in the third row of the table above.
So let's now practice going the other way, converting an effective rate
into a nominal rate. Again, the loan amount is 10,000.
Not a 100,000, sorry, 10,000. The annual effective interest rate. Well,
let's pick up what we've just calculated, because we know that if we convert
it into a nominal rate, we should get 10%. The frequency is four again,
and the term is one. So what are the key inputs that we
need? We need the annual effective rate of 10.38, and we need the
compounding frequency of four, and there we can see the formula for the
nominal rate, if we know the effective rate, and it's quite challenging,
so we have to be really careful putting it in, and that's the
benefit or having it just below the cell there. So we're going to start
by equals[bracket one plus the effective interest rate] all raised to the
power of one divided by the compounding frequency, close bracket minus 1,
close our final bracket and annualize it by multiplying that by the compounding
frequency. And when we do that, we can see that we get a
nominal rate of 10%, which is the result that we were expecting.
2. Let's practice!