Question

Orca Research made an initial deposit into an account paying 3% compounded annually. Orca withdrew $4421 at the end of year 5 and made a deposit of $6629 at the end of year 7. By the end of year 12, Orca had $66251 in the account. What was Orca's initial deposit?

Answer 1

@zepdrix

Answer 2

I have a solution but it was wrong.=(

Answer 3

Hmm thinking :d

Answer 4

\[\large\rm A(t)=P\left(1+\frac{r}{n}\right)^{nt}\]So we're trying to figure out this P value,
the amount initially put into the account. The principle amount.

Answer 5

Yessss

Answer 6

And they told us that our rate, is 3%
\(\rm r=.03\)

And that the number of compoundings yearly, is just one, (annual compounding),
\(\rm n=1\)

Answer 7

So our formula simplifies down a little bit,\[\large\rm A(t)=P(1.03)^t\]Ok with that part? :o

Answer 8

Okay

Answer 9

yes I know how you get that

Answer 10

F = P(1+i)^n

Answer 11

F = P(1+0.03)^n
F = P(1.03)^n

Answer 12

So then we have some weird stuff going on.
At t=5 years we have,\[\large\rm A(5)=P(1.03)^5\]But notice that 4421 was `taken out of` the account at this point,\[\large\rm A(5)=P(1.03)^5-4421\]

Answer 13

Hmm I think it gets a little tricky after that, thinking :p

Answer 14

Here let me show you what I got as you are thinking.

Answer 15

k

Answer 16

[[P(1.03)^5-4421]*(1.03)^2+6629]*(1.03)^5 = 66251

Answer 17

shoot that doesn't work...

Answer 18

Hmm that's what I'm coming up with also...
good good good. good job.
But it's leading you to an incorrect answer?

Answer 19

hold on

Answer 20

P = 44890.72

Answer 21

Is that what you got?

Answer 22

44890.72825 ya

Answer 23

It's a solution I even checked....

Answer 24

I did this last time and got it wrong. We have three attempts per problem. My logic is correct right?

Answer 25

Yes,
but it's possible we're misinterpreting something in here :)
thinking

Answer 26

It's not as straightforward as trying to find the future value. When finding the present value it's important to remember that anything that happens on the time line has not happened to the present value, but it did happen to the future value. We have remember that as we take the future value and work backwards. A good way to check, once you have your present value, is calculate the future value based on the cash flow. It should be approximately equal to the future value given. If you want me to check your equation, just let me know.

Answer 27

This is what my instructor said over an email after I ran her my last solution.

Answer 28

are you timed?
I just need a few minutes to try this other approach

Answer 29

I am not timed. lol

Answer 30

the teachers explanation doesn't make sense to me lol

Answer 31

Haha same.

Answer 32

Still thinking?

Answer 33

ya

Answer 34

darn that didn't work :d hmm

Answer 35

ok imma go eat some food,
maybe look at this later :\
sorry I'm out of ideas :c

Answer 36

anyone other smarty pants online? :d

Answer 37

It's okay I am going to her office hours in 30 min

Answer 38

cool :)

Answer 39

Thanks though