>> We're going to work with compound interest again.
Here's the formula.
A is the amount in the account after t years.
P is the principal.
r is the annual interest rate.
n is the number of times that the interest is compounded per year.
And t is the time in years.
If the interest is compounded annually, then n is 1.
Semiannually, n is 2.
Quarterly, n is 4.
Monthly, n is 12.
And daily, n is 365.
You do not need to memorize this formula.
But you do need to know these values down here.
This time, instead of solving for A or P, we will be solving for r.
We will be asked to find the interest rate.
Find the interest rate if $1600 is compounded annually and that grows to 1764 in two years.
So here's your formula.
So the amount at the end of the time is 1764.
The principal is 1600.
The interest rate is unknown.
It's compounded annually, so n is 1.
Two years, so t is 2.
Let's clean that up.
So we have a quadratic equation.
It's kind of messy though.
Let's write another quadratic equation similar to it but with smaller numbers.
So instead of 1764, I'm just going to write 10.
Instead of 1600, I'm going to write 5.
Instead of r, I'll write x. How would you solve this quadratic equation?
Well, the next step on this quadratic equation would be to divide by 5, right?
Because you want to get that perfect square by itself.
Well, that's the same step that we need to do over here on our equation.
We have to divide by the 1600 to get our perfect square by itself.
So we cancel the 1600s.
So let's simplify this.
So 1764 over 1600.
That's kind of messy.
A lot of people at that point are going to pull out their calculators,
but you don't want an approximation.
You don't want an approximation and another approximation after that,
so don't take your calculator out until the end.
So just leave that there.
At that point, on either of these equations, the next step would be
to take the square root of both sides, right?
So over here, we're going to take the square root,
so plus or minus the square root of this big fraction.
And then we move the 1 to the other side.
So r is equal to, and I'm going to put the negative 1 in front, so negative 1 plus
or minus the square root of that fraction.
And there's no need to simplify this because it's going right in the calculator.
All right, so now I'm going to pull my calculator out.
So in my calculator, I'm going to have negative 1 plus
because I know it's not going to be the negative.
Because negative 1 minus the square root is going to end up being a negative answer.
Our interest rate's not going to be negative.
So negative 1 plus the square root of, and if your calculator does not automatically put
in parentheses, you need to put that parentheses for it,
then 1764 divided by 1600 close parentheses.
Because you need to have the calculator take the square root of the whole thing, then hit equals.
And you will get .05.
Normally you're going to have to round, but this came out exactly .05.
The interest rate.
Is five percent, once you change that to a percent.
Something else to note.
A lot of students will take this right here, and they will distribute the 2.
They'll say that this is 1 squared plus r squared.
Be careful, you can't do that.
You cannot distribute an exponent across addition or subtraction.
Okay? You cannot do that, so be very careful.
Note this rule right here that the square of a plus b is not equal to a squared plus b squared.
Please not that we found that MyMathLab is grading the problems wrong in this section.
Instead of having you separate the real and imaginary parts,
they are only giving you credit if you keep them together.
In other words, 3/4 plus 1/4i is the correct way to write the answer.
But they are only giving you credit if you write it as the quantity 3 plus i over 4.
At least in the current version of MyMathLab as I make this video.
I'm sorry about that.
So as you're heading towards your homework and your quizzes,
please be sure to do it in this way.
When you get to my exams, I'll accept it either way because of this inconsistency.
Another thing to note, on MyMathLab for some reason, they are only accepting i
in front of the radical and not behind.
It is perfectly mathematically correct to put the i in front or behind the radical.
Both of these answers is perfectly correct.
2 plus i times rad 3.
2 plus rad 3i is perfectly fine.
As long as you do not have the i under the radical.
They are only accepting i in front of the radical.
So be sure to write your answers like that for MyMathLab.