1. Title Slide
So far, we've looked at compounding a present value using different compounding
periods, but always over one year. What about when the investment horizon
is greater than one year? To figure this out, let's use the scenario
where we have a PV $1000, a nominal interest rate of 10% with
quarterly compounding. But this time, let's have a three year investment
horizon. So now, n equals three. Perhaps, and surprisingly, our formula
is going to look very similar because the interest earned each quarter will
still be the same, 10% divided by four,
is before the number of compounding periods we earn this over will be
based on the number of years n and the compounding frequency IF.
Because this is a three year investment, n equal three, IF is still four,
so n times four 12. Our future value after three years is 1344.89, and
we can check this by popping back into Excel. So here we are
back in our Excel workbook for the chapter, and I've scrolled down to
the next section where we're trying to find the future value when n the
number of years is greater than one. Thinking about the example that we
just walked through, we had a present value of 1000, a nominal entry
of 10%, and we've got quarterly compounding interest. So frequency is four
and the number of years, we're trying to find the future value of three
years from today. Again, we've got the algebra formula for the future value
there, so we step by going equals, the present value times[one plus the
nominal rate, all divided by the frequency, all raised to the power of
the number of years, times the frequency]. And you can see they've got
1344.89. So let's just confirm that with the IF vFunction, we're gonna get
the right per period, we're going to get the number of periods.
There's no payments being made or received along the way, so PMT is zero,
we know the present value, and the type is always a zero for
compounding at the end of the period, and we get 1344.89 again. At
least just practice using a different example where the present value is
a 1000, where only a nominal interest rate of 10% so, but now
we've got monthly compounding, so the frequency is 12, and we're trying
to find the future barely five years from today. So, what's the future
value? Well, it's the present value times open[one plus the nominal interest
rate divided by the frequency of 12] all raised to the power of
n, the number of years, times IF, the compounding frequency, close bracket.
And you can see that we're going to have 1645.31 in five years
time with those inputs, at least just confirm this using the IF vFunction,
the rate... It's the rate period, 10% divided by the compounding frequency,
the number of periods is the number of years,
times their compounding frequency. We're not making or receiving any payments
during that five years, so PMT is zero and the present value is
a 1000, and as always, the type is zero for compounding at the
end of each monthly period, and we see we have the same result,
1645.31.
2. Let's practice!