Question

An investment account earns 4% per year compounded annually if the initial investment was $4000 how much is the account after three years? Round your answer to the nearest dollar

Answer 1

\[I = P \times R \times T\]

This is the equation for simple formula. Let I represent interest, P the principal, R the rate of interest, and T the time.

Answer 2

Now plug in what the data that you do have.

Answer 3

@HannahC234 Are you still there?

Answer 4

Yes thanks!!

Answer 5

Ok, great, so we know that you started with 4000 dollars, this is what we would put for "P", or, principal in the equation. We know that the rate is 4% per year, this will be plugged into "R", or rate, just remember to convert 4% into a decimal. Then lastly we want to know the amount of interest after 3 years, so plug in 3 years represented by months (12 x 3).

Answer 6

Okay but I thought the formula was A=P[1+(r/n]^nt

Answer 7

I'm so sorry, I read a bit too fast and I assumed your question was asking something different. You are right! The formula I provided was for simple interest. Let's go ahead and start over with the actual formula!

Answer 8

\[A = P(1+\frac{ r }{ n })^{nt}\]

There we go. So now, first thing we want to do is find out what to plug in. Can you tell me what the values are for:

P =
R =
N =
T =

Answer 9

P=original amount (4,000)
R=The rate as a decimal (.04
N= The number of times per year (1?)
T=Time(3?)

Answer 10

Yes that's perfect! It does not tell us the interest is compounded monthly, quarterly, etc.. it simply tells us it is compounded annually so it will b 1 for N. And since we want to know the total in 3 years the 3 is also correct. Now, let's plug that in.

\[A=4000(1+\frac{ .04 }{1})^{1 \times 3}\]

Answer 11

Now first step is to clear that parenthesis, (you know, PEMDAS).

So, what's .04/1?

Answer 12

.04?

Answer 13

What I have is
A=4000(1+.04/1)^1x3
A=4000(1+.04)^1x8
A=4000•1.04^1x8
A=4160^1x8
And now I'm stuck is this right so far?

Answer 14

Sorry for the long waits, I'm multitasking. Anyways, where did you get the 1x8?

Answer 15

Oh it's supposed to be 1 and 3 sorry

Answer 16

Yes, and also, don't forget PEMDAS! you multiplied 4000 and 1.04 before you cleared the exponent for 1.04.

So this is what you have now:
\[A = 4000(1.04)^{3}\]

Clear the exponent first! Now what do you get?

Answer 17

I'm pretty sure this is wrong because I did 1.04^3=1.12
And then 4000x1.12=5039

Answer 18

Watch out for the text. It says, "round your answer" don't round 1.04^3, that would be 1.124864

Answer 19

So now,

\[A = 4000(1.124864)\]

Answer 20

And that right there would be your answer! You know exactly how to do this, you just need to watch out for the order in which you do this.

Answer 21

So I got A=4499,456
What would I round that to?

Answer 22

Now you round that to the nearest dollar, like the questions says. So what is that rounded up to nearest dollar? (Whole number)

Answer 23

4500?

Answer 24

Yes! That's perfect.

Answer 25

That you so much!!!!

Answer 26

Thank^^

Answer 27

No problem! Sorry if it took a while, I like to make sure the asker knows how to do it. Just remember to watch the order in which you do it!