1. Title Slide
Let's summarize what we've explored together in the first two lessons of
this chapter, this time using a little bit of algebra.
In the example so far, the present value, or our starting amount,
has been $1000 and our nominal interest rate has been 10%.
We want to find the future value, so we are compounding forward in
time. I want to consider specifically the quarterly compounding scenario,
so f is four. Also, we want to find the future value in
one year's time, so n equals one. If you recall from the table
we created in Excel earlier this chapter, we start by taking the PV
and multiply this by one plus the nominal interest rate divided by the
compounding frequency f, and we do this for every compounding period.
The number of compounding periods will be based both on the number of
years n, and the compounding frequency f. So, we need to take the
nominal interest rate I, divide it by the compounding frequency f,
and add this to one. We then raise all of this to n
times f. Putting the values in for PV, I, n, and f,
in this example, the future value is 1103.81. Now, I'm going to switch
back to Excel and do this example, and it would be great if
you try to follow along with me. I'm also going to solve this
question using the Excel FV function. And just to make doubly sure you've
got this, we'll do a second example using different inputs. So,
here I've opened up my workbook and I've scrolled down to the session
called Future Values Using Compound Interest Where N Equals One. In other
words, finding the future value one year from today. Just thinking about
the example we just walked through, the present value was 1000,
the nominal interest rate is 10%, the frequency is four because we're using
quarterly compounding, and the number of years in the future, remember,
is one. So we want to find the future value one year from
today. In cell D51, we've got the algebraic formula for the future value,
and we can say that it's equals the present value times open bracket
one plus the nominal interest rate I, divided by the compounding frequency
f, and we're going to raise all of that to the power of
the number of years n times f, and we close bracket,
and we see we get 1103.81, which confirms our result. We can also
use the future value function. Remember to put a minus at the front
to make sure your result's positive. The rate per period is the rate
per year, the nominal interest rate divided by the number of compounding
periods within the year. The number of periods is the number of years
times the number of compounding periods within the year. We're not making
or receiving any payments during the year, so the PMT input is zero,
the present value is 1000, and as always, our type is zero because
we're compounding at the end of each quarterly period, and we get 1103.81.
So, let's have a look at another example. It's the same inputs,
but this time we're going to have monthly compounding. So, the present value
is 1000, the nominal rate is 10%, and the frequency is 12. The
number of years is one. Now, if you want to have a go
at this yourself, press pause and have a go, and then press play
when you're ready to confirm, otherwise, I'm just going down through it
now. The future value equals the present value times open bracket one plus
the nominal interest rate divided by f, all raised to the power of
n times f, and we can see that we get 1104.71, which confirms
our result from earlier this chapter. And then we can use the FV
function, negative FV, open bracket, we take our nominal rate and divide
that by twelve for the rate per period. The number of periods is
the number of years times the number of compounding periods. The payment
is zero, the PV we know is 1000, and the type as always
is zero, and we get the same result, 1104.71.
2. Let's practice!