Question

Determine the amount needed to be deposited today(as a one time deposit) in order to have $35,000 four years from now. At 8%
Solve for:
Compounded: Annually
Semi Annually
and Quarterly

Answer 1

So a basic compounding without any added investments. Know the formula?

Answer 2

http://qrc.depaul.edu/StudyGuide2009/Notes/Savings%20Accounts/Compound%20Interest.htm

Answer 3

OK, you see the formula and you have expressed you have a problem with "Annually Semi Annually and Quarterly" So the issue is translating what the question is asking, right?

Answer 4

yes, when it comes to words/story problems I have a very difficult time. I looked at the formula you sent, but I don't understand it. I see things differently, I need an answer and then I tend to work the problem backwards, that is how I do math...strange I know.

Answer 5

Actually, they gave you the answer this time. They want you to find P.

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

P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year

That last one, n, is the key to those terms.

Anniually means n=1
Semi Anniually means n=2
Quarterly means n=4

Now, "A = amount of money accumulated after n years, including interest." That is where you want to be at. They give that to you as $35,000.

Answer 6

So, start replacing things in:\[A=P\left(1+\frac{r}{n} \right)^{nt}\]With what was given, and check with me if you have the right thing in the right place.

Answer 7

A= 35,000(1 + 4/1)

Answer 8

They are giving you A, they want you to solve for P.
Also, a problem with r and t there.

r is the rate, so the PERCENTAGE rate, but as a decimal. That help?

And t is Time in Years.

Answer 9

35,000*.08*4 ?

Answer 10

Well, closer. I will use the math thingie here.
\[35000=P\left(1+\frac{.08}{n} \right)^{n4}\]
Now, the n depends on which one of the three you are doing. So 1 for the annually. You need to solve for P.

Answer 11

I am completely lost...this is why it takes me so long to pass math, I am so bad with it. I have been here trying to figure it out and I have become frustrated.I am the type that has to see it done, and then I try doing it. Thank you for your time, I really appreciate it.

Answer 12

Well, then let me look at the first one.
We have this right now:
\[35000=P\left(1+\frac{.08}{n} \right)^{n4}\]
And n is 1 for the first one, so:
\[35000=P\left(1+\frac{.08}{1} \right)^{1\times 4}\]
Which simplifies pretty easy:
\[35000=P\left(1+.08 \right)^{4}\]
And a little more:
\[35000=P\left(1.08 \right)^{4}\]
Now, to solve for P, we need P alone, so I need to divide off what is multiplying P.
\[\frac{35000}{\left(1.08 \right)^{4}}=P\]
And that can go into some calculators, but if not, I take one more step, do the power.
\[\frac{35000}{1.3605}=P\]Which is rouded off to enough decimals that it won't cause a problem.

Answer 13

25,725 ?

Answer 14

I got 25,726.04 for the first one. So basically the same.

Answer 15

ok..so let me try semi

Answer 16

kk.

Answer 17

35000/1.8509=18909.7

Answer 18

Hmmm... Remember, it only simplified so much because n was 1. When n is 2, it changes things.