Question

Suppose that ​$30,000 is invested at 9​% interest. Find the amount of money in the account after 5 years if the interest is compounded annually.

Answer 1

need help setting up the equation :c

Answer 2

The compound interest formula is

\[\LARGE A = P*\left(1+\frac{r}{n}\right)^{n*t}\]

where,

A = final amount in account after t years
P = amount deposited
r = interest rate
n = compound frequency (how many times you compound interest per year)
t = time in years

Answer 3

so how would n work? you would compound it 12 times correct? or wait is it 5?

Answer 4

After every year, the value of the account will increase by 9%, multiply by 1.09, so you can take the initial amount at t=0 years, P=30000, and it forms the exponential

A = P*(1.09)^t

Answer 5

ohh I think 5, right?

Answer 6

`the interest is compounded annually`

so you compound 1 time per year @milliedelongg

so n = 1

Answer 7

but it says five years. does that matter? would it still be one?

Answer 8

after plugging in n = 1 and r = 0.09, it will simplify to what @DanJS wrote out

After that, plug in t = 5 because we want the amount after 5 years

Answer 9

or you can just plug in everything at once. It's up to you

Answer 10

ohh okay I understand

Answer 11

I got 46,158.72 (rounded to nearest cent)

Answer 12

same here

Answer 13

nice work

Answer 14

okay coolio thank you so much!!!!

Answer 15

you're welcome

Answer 16

can you help me with another one? this one doesn't give me a N

Answer 17

sure go ahead

Answer 18

5000 is invested at 4% "continuously" for 7 years

Answer 19

the keyword "continuously" means n essentially heads off to infinity. Basically you compound every chance you get, ie, as much as possible

You'll use this formula now

\[\LARGE A = P*e^{r*t}\]

the 'e' is a constant that is a lot like pi = 3.1415...

e = 2.71828182846

and that decimal expansion goes on forever without a known pattern

Answer 20

to get the best accuracy, it's best to use the built in "e" button on your calculator

Answer 21

I got 5020.49

Answer 22

what calculator do you have?

Answer 23

ti-84

Answer 24

did you type the 2ND button and then the LN button to get the 'e' ?

Answer 25

ohhh that e has a exponent thing

Answer 26

yes tell me what you get when you retry

Answer 27

I still got the same answer. what are you getting?

Answer 28

you should have 5000*e^(0.04*7) typed in

Answer 29

ohh I had it in wrong

Answer 30

do you remember how to show the limit used here for e in another tab when you free?