### Video Transcript

An investment account offers
two-percent compound interest. The following formula can be used
to calculate the interest earned on the investment after 𝑛 years. 𝐼 equals 𝐴 naught multiplied by
1.02 to the power of 𝑛 minus one. 𝐼 is the amount of interest. 𝐴 naught is the amount initially
invested. Sandy invests some money for six
years and receives 2535 pounds and 14 pence interest. Calculate the amount of money Sandy
initially invested, giving your answer to the nearest 100 pounds.

We’ve been told that Sandy invests
her money in an account that offers two-percent compound interest. It might be tempting to try and
recall the formula that we generally use when working with compound interest. However, we’ve actually been given
a slightly different formula. It looks somewhat similar to the
formula that we normally use, but this time it only calculates the interest
earned. So rather than being a compound
interest question, this is actually a substitution and solving question. Let’s see what else we know.

We’re told that Sandy invests her
money for six years. So in this equation, our value of
𝑛 is going to be six. The amount of interest she receives
at the end of that time is 2535 pounds and 14 pence. So in our equation, 𝐼 is going to
be 2535.14.

Let’s substitute what we currently
have into this formula then. If we replace 𝐼 with 2535.14 and
𝑛 with six, our equation becomes 2535.14 equals 𝐴 naught multiplied by 1.02 to the
power of six minus one. This question is asking us to
calculate the amount of money Sandy initially invested. That’s 𝐴 naught. So we’re going to need to solve
this equation by performing a series of inverse operations.

To figure out what inverse
operations we need to apply, let’s look at what’s happening to 𝐴 naught. It’s being multiplied by 1.02 to
the power of six minus one. So to solve this equation for 𝐴
naught, we need to divide both sides by 1.02 to the power of six minus one. And of course, we could evaluate
that by typing 1.02 to the power of six minus one into our calculator.

Alternatively, we can leave it as
it is and work this out as one big sum at the end. Let’s do the latter. We get that 𝐴 naught is equal to
2535.14 all over 1.02 to the power of six minus one. Now at this point, you’ve probably
noticed we don’t need the extra set of brackets around the 1.02 to the power of six,
though it doesn’t actually make a difference whether we include them or not at this
stage.

Our final step is to work out the
value of 𝐴 naught by typing 2535.14 all over 1.02 to the power of six minus one
into our calculator. This should be fairly
straightforward on a scientific calculator. If you’re not working with one of
those then, remember, this fraction line means divide. So you’ll need to work out 1.02 to
the power of six minus one and then do 2535.14 divided by that number. If that’s the case, you’ll be
performing the calculation 2535.14 divided by 0.126162 and so on. Either way, we should get a value
for 𝐴 naught as 20094.256 and so on.

We need to round our answer to the
nearest 100 pounds. This is the one hundreds
column. So we look to the digit immediately
to the right of this. That’s called the deciding
digit. Remember, if that deciding digit is
five or above, we round the number up. If it’s less than five, we round
the number down. This time, the deciding digit is
greater than five. So we’re going to round our number
up. And this means the amount of money
that Sandy initially invested was 20100 pounds, correct to the nearest 100
pounds.

And we could of course check our
working by substituting this back into the original formula. That’s 20100 multiplied by 1.02 to
the power of six minus one. That gives us an answer of
2535.86. Remember, we rounded, so it would
make sense that our answer is just a little bit out from the original interest we
were given. That was 2535.14. So again, we can see it’s fairly
close, so we’ve probably done this calculation correct. The original amount of money she
initially invested is 20100 pounds.