1. Calculating FV Using Simple Interest
The time value of money is crucial in the world of finance,
financial markets, and investing in general. Let's explore why by revisiting
our simple interest example. Imagine that we have $100 to invest today or
at year zero. This investment earns simple interest of 5%
per year. How much will we have in three years time?
Well, after one year, we receive interest of $100
multiplied by 5%, which equals $5. We add this interest to our initial
$100 to get $105. The same process repeats for each subsequent year,
meaning that after two years, we have $110 and after three years,
we have $115. Now, let's use the language associated with the time value
of money and call the amount that we have today, at year zero,
the present value or the PV of our investment.
Our challenge is to find the future value or FV after three years.
Well, FV can be expressed mathematically as the $100 we have in year
zero plus bracket $100 multiplied by 5% simple interest multiplied by three
years close bracket. This gives us a general equation that the future value
equals the present value plus bracket the present value multiplied by i
multiplied by n close bracket. We can use some algebra and rearrange this
formula to be the future value equals the present value multiplied by bracket
one plus i multiplied by n close bracket.
Now, let's see if we can do this calculation in our Excel workbook.
So here we are, back in the simple and compound interest template workbook.
I've scrolled down a little bit, but you can still see the previous
exercise that we walked through together with a total amount that we owed
the bank was 115, you see that in cell G14. So let's just
scroll down to our next example. We want to calculate the future value
using the two formulas that we just saw in the video.
And the two formulas that we just saw in the video,
I've written here in red, and so we've got the future value equals
PV plus bracket PV times i times n close bracket, and then remember
we can rearrange that to get the formula here, which is
the PV times bracket one plus i times n close bracket.
Alright. So let's have a think about our inputs first of all,
and remember we had a present value of a 100.
We had simple interest of 5%, and we had a three year team.
So what would the future value be? Remember, we want this to work
out to be 115. So the future value equals the present value,
so I'm just going to reference the present value plus[and we have the
present value again times the simple interest rate,
which is 5% times the term, which is three years].
And you can see that when we do that again, we get 115,
so that works just nicely. Let's see if we get the same answer
with the rearranged future value formula, where we start again with the
present value, and this time we multiply it by[one plus the interest rate,
which is 5% multiplied by the term three]
and we should get a 115 again, which we do. So here we
can see that both of those future value formulas work. So if you
watched the video, I really encourage you to give this a go now
just to make sure that you can get the same answer as you
see on the screen.
2. Let's practice!