1. Calculating PV Using Simple Interest
In the last lesson, we used a simple interest to find the future
value for a given present value, but often in finance, we know the
future value already and we need to find the present value instead.
So now, suppose we know we need $115 in three years time for
something really important, how much do we need to invest today if the simple
interest rate is 5%? Because we did some work earlier, we know that
the simple interest is $5 per year, and we could simply subtract the
simple interest earned each year from $115. But we can also rearrange this
future value formula and make the present value the subject of the equation.
If you want to give this a go now, pause the video and press play to see
the answer. When we do rearrange the formula, we get that the present
value equals the future value, multiplied by 1 divided by bracket 1 + i
× n close bracket. Using some algebra again, this can also be written
as the present value equals the future value divided by bracket 1 +
i × n close bracket. Now, just to remind us all of what these
letters mean, the future value is "FV", the present value
is "PV", "i" stands for the simple interest rate, and "n"
is the number of periods or years of
our investment. So, let's use these PV formulas and apply them to a
new example, which should help us test our understanding. Imagine that someone
promises to pay you $100 but you have to wait for five years,
and let's say that the simple interest rate
is 4%. What would the amount be worth today? In this scenario,
we're using $100 as the future value. And after crunching the numbers,
we find that the present value is 83.33. Now, let's double check our
present value calculations using Excel. So, we're back in our workbook,
and you can see on the left the future value calculations we looked
at an earlier lesson. Now what we are going to do is we're
going to calculate the present value using simple interest. And just to
remind you, we've got a slightly different input. It's a different example.
This time we're going to start with the future value
of 100. This time the simple interest rate
was 4% and the term was five years. So it's a different example
to what we've been using previously, and we want to use those inputs,
the future value, the simple interest, and the term, to find the present
value using the two formulas that we just introduced. So the first formula
we can see there in cell H22 is the present value equals the
future value times 1 divided by bracket 1 + i × n close bracket.
So let's have a look to see if we can find the present
value, the present very equals the future value of 100. So,
in five years time we've got $100, times 1, divided by, and in Excel
you do "divided by" by a backslash, open bracket, 1 plus the simple interest
rate of 4%, times n which is the term of five years.
And if we close that bracket we should see that the present value
equals 83.33. So what this means, remember, is if we had 83.33 today and
we earn 4% simple interest for five years, at the end of the five
years we'll have the future value of 100. Now we can rearrange that,
remember, to get the present value equals the future value divided by 1 +
i × n close bracket. So let's just make sure that we get
83.33 again with this rearranged formula. So I'm going to start with the
future value of 100, and I'm going to divide that, remember,
backslash, by open bracket 1 plus the simple
interest rate of 4%, times the term of five. And when I select
the enclose bracket and hit enter, I can see that,
2. Let's practice!