Question

Can I get help on how to start solving this, along with the formula? Studying for Midterm tomorrow.

Aimee currently has an account balance of $2,199.21. She opened the account 9 years ago with a deposit of $1,668.17. If the interest compounds quarterly, what is the interest rate on the account?

Answer 1

@zepdrix

Answer 2

@Awolflover1 @samanthagreer @quickstudent

Answer 3

What do you think it is

Answer 4

The formula?

Answer 5

or?

Answer 6

the anwer

Answer 7

i don't know...

Answer 8

I don't even know what formula to use.

Answer 9

Anything appreciated.

Answer 10

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

P is our principle or starting amount
r is the interest rate
n is the number of compoundings per period
t is the period (number of years in this case)
A is the amount we end up with.

Answer 11

They gave us a bunch of the pieces, and they expect us to solve for the unknown piece, which is r in this case.

Answer 12

in this situation, just for personal preference, can we use x?

Answer 13

For your unknown? Sure!\[\large\rm A=P\left(1+\frac{x}{n}\right)^{nt}\]

Answer 14

okay lemme plug everything in and try to solve, then can i check back?

Answer 15

Do you understand the value of each part that they gave us?

t = 9 years
P = 1668.17
n is a little tricky. quarterly means we'll be calculating it 4 times a year, ya?

Answer 16

Oh!!!! I tried to solve this with that formula!

Answer 17

yes i do!

Answer 18

correct!

Answer 19

the problem i came to was when we get \[2,199.21=1668.17(1+\frac{ x }{ 4 })^{36}\]

Answer 20

the \[\frac{ x }{ 4 }\] How do i deal with that thing?

Answer 21

@zepdrix

Answer 22

Ahh sorry was making a sammich >.<

Answer 23

no youre fine! Just checkn!

Answer 24

\[\large\rm 2,199.21=1668.17\left(1+\frac{x}{4}\right)^{36}\]Hmm bunch of weird stuff being applied to our x.
We'll have to undo all of this, one step at a time.
Notice this big block of stuff is being `multiplied` by 1668.17.
So we'll have to `divide` both sides by this value to undo that step.

Answer 25

Because of order and operations duh!

Answer 26

i should've know that to begin lol

Answer 27

\[\large\rm \frac{2199.21}{1668.17}=\left(1+\frac{x}{4}\right)^{36}\]Ok with that step?

Answer 28

1.3183?

Answer 29

\[\large\rm 1.318=\left(1+\frac{x}{4}\right)^{36}\]Ok.
So the `division` took care of that `multiplication`.
Now we need to somehow deal with this `exponent`.
Do you remember how to get rid of an exponent?

Answer 30

oh god, i dont :-(

Answer 31

We undo `powers` using `roots`.

For example if we had an equation like this: \(\large\rm x^2=4\)
We would undo the `square` on the x by taking a `square root` of each side.\[\large\rm \sqrt{x^2}=\sqrt4\]\[\large\rm x=\pm2\]

Answer 32

We have a 36th power,
so we'll need to take a 36th root of each side.

Answer 33

im horrible at roots, but i think i remember some things about htat stuff. I wouldn't know how to continue from here though

Answer 34

\[\large\rm \sqrt[36]{1.318}=\left(1+\frac{x}{4}\right)\]So we'll take a 36th root of each side, that will undo the 36 power on the right side of the equation.

Answer 35

If you use your calculator, you should get something like 1.007699 on the left side of the equation. Maybe we'll round that to 1.008

Answer 36

\[\large\rm 1.008=\left(1+\frac{x}{4}\right)\]

Answer 37

could we solve without roots?

Answer 38

i think i have the answer though : 3.1% ?

Answer 39

I'm coming up with x=0.032 which is 3.2%
(But that was with the rounded values, so maybe yours is more accurate).

Answer 40

without roots? Hmm I don't think so :o

Answer 41

Yayyy team, we did it! :)

Answer 42

Thank you for your help!