Question

Ok, so I'm answering a question for my quiz and I have trouble plugging numbers into the formula
A(t) = P (1+ r/n) ^ nt

Can anyone tell me what the variables stand for? I know P is the principle, or the number before rates and stuff.. I'm not sure where the converted percentage goes though

Answer 1

Oh and I know T is time... But I'm unsure about A, r, and n?

Answer 2

P is the `principle`, the starting amount.
t is the `time` measured in some period, usually years.
r is the `rate` of interest or increase.
n is the `number of compounds per period/year`.

Answer 3

Do you remember the question from your quiz? :o
Or do you have it in front of you?

Answer 4

Maybe you can use that information to fill in the pieces :x

Answer 5

Oh I have it if you want to help me write out my formulas, give me a second

Answer 6

Oh also,
A is the `amount` that you have after some time t.

Answer 7

5.Using the function A(t)=P(1+r/n) ^ nt create the function that represents your new car loan. The principle will be the price of the vehicle you selected, not how much you are putting down.
6.Use your function to determine how much you will owe the bank in five years. This is assuming you are not paying down your loan, so do not get scared! Show all of your work.
7.Again, we are assuming that you are not paying down your loan, and the bank's interest keeps piling on. Being a smart financial planner, you want to figure out how many months it will be until you owe the bank an amount of $100,000.00. Solve for t and show all of your work.
8.Lastly, you decide to keep track of your loan weekly instead of monthly. Solve for the adjusted interest rate.

Answer 8

From what you said, my rate is 6% or 0.06, my principal is 14700, and I'm not sure what n is :/

Answer 9

Oh wait, it's 12 because it's monthly

Answer 10

Calculated monthly? Ok cool :)

Answer 11

So far I have A(t)=14700(1+0.06/12)^12t
I'm not sure if that's right

Answer 12

Mmmmmm yah it looks like you're on the right track!

Answer 13

Okay, so if that's right then the next question is A(5)=14700(1+0.06/12)^12(5)

Answer 14

Mmm good good.

Answer 15

Trying to solve it and I'm not sure if I'm doing it right :/.

A(5)=14700(1+0.06/12)^12(5)
A(5)= 14700(1+0.005)^60
A(5)= 14700(1.005)^60
A(5)=14700(1.35)
and the 1.35 is rounded

Answer 16

k cool, looks good so far :o

Answer 17

Thanks! Just one more problem I'll ask you to check and I'll give you a medal ^_^

Answer 18

Understand part 7?
That one is a little trickier :O

Answer 19

To set up number 7, should I set A(t) to 100,000(t)?

Answer 20

A(t)=100000

So your setup will look something like:
100000 = 14700 ( 1 + .06/12 ) ^ (12t)

And then we need to solve for t from there.

Answer 21

Thank you! c: I'll work that out then

Answer 22

Okay. So I'm down to 100000 = 14700 (1.005)^12t
I'm not used to solving equations with exponents yet... So, should I try to turn 12t into a normal number rather than exponential first? Or should I subtract first? or.. divide? Really hoping I don't have to take any logarithms here because I don't have a full understanding of them

Answer 23

Yes you'll want to use a log I'm afraid :c
But first we would divide the 14700 to the other side.

Answer 24

Life is cruel :c.
But furthermore, 6.80 = (1.005)^12t is what I have so far

Answer 25

Ok good, we'll take the natural log of each side,\[\Large \ln 6.8\quad=\quad \ln\left[(1.005)^{12t}\right]\]

Answer 26

I know they're scary, but it's just a simple step so far.
We're just wrapping each side into a log.

Answer 27

We'll have to use properties of logs to move some stuff around, but after that, we can leave all of the work up to Mr. Calculator.

Answer 28

For the natural log of 6.8 I got 1.92 (rounded) and the other side I'm not sure how to input into my calculator. Part of the reason logs bother me. I have a TI-84 Plus if you have any idea D:

Answer 29

No calculator just yet! :O

Answer 30

Got some stuff to do first.

Answer 31

By the way, I really appreciate you helping me for so long here. If I could I would get you thousands of fans but I can't, so I'll give you a medal and I already became a fan

Answer 32

An important rule of logs:\[\Large\bf \log(a^{\color{orangered}{b}})\quad=\quad \color{orangered}{b}\log(a)\]This rule allows us to bring the exponent down as a factor in front of the log.
Do you understand how me might apply that to our problem here?\[\Large\bf \ln 6.8\quad=\quad \ln\left[(1.005)^{\color{orangered}{12t}}\right]\]

Answer 33

I should have used ln instead of log for the `rule of logs` so there wouldn't be any confusion.. my bad.

They are the same thing though.

Answer 34

So... 12t ln (1.005)?

Answer 35

\[\Large\bf \ln 6.8\quad=\quad \color{orangered}{12t}\ln\left[(1.005)\right]\]Ok good.

Answer 36

Then just a few more steps to solve for t.

Answer 37

So, when inputting this into my calculator do I just put 12 instead of 12t?

Answer 38

\[\Large\bf \ln 6.8\quad=\quad \left[12\ln(1.005)\right]t\]
I prefer to solve for t BEFORE putting anything into the calculator, but maybe that's just me.

Answer 39

So that junk on the t, we need to divide it to the other side.

Answer 40

I'll be honest and say my head is spinning again, xD.

Answer 41

So the rule of logs allowed us to take the t outside of the log.
So on the right, we just have 3 things being multiplied together.

12, t, and ln(1.005)

So we'll divide each side by 12,
then divide each side by ln(1.005),\[\Large\bf \frac{\ln 6.8}{12\ln(1.005)}\quad=\quad t\]

Answer 42

Too much? :o

Answer 43

No, this looks better. Thank you!

Answer 44

Then mr calculator should be able to do the rest of the work \c:/

Answer 45

I have one more question though :c. It's the last one on this assignment, and when I read it I had no idea where to start. I kind of wish I could skip it

Answer 46

8. Lastly, you decide to keep track of your loan weekly instead of monthly. Solve for the adjusted interest rate.
I think this changes n to 52

Answer 47

hmm

Answer 48

ok n=52, hmm
I'm trying to see how that will allow us to solve for a new rate... hmm

Answer 49

I don't think it's too easy considering it doesn't give many variables >.< It's okay if it's too much, I mean you've already helped me a lot. I don't mind turning it in as is or asking my teacher for help

Answer 50

At time t=0 we know that A(t) = 14700.
But that doesn't allow us to solve for r. Hmm.

At t=1,\[\Large A(1)\quad=\quad 14700\left(1+\frac{r}{52}\right)^{52\cdot1}\]Are we supposed to assume something about A(1) maybe?
Does it give us the same value as before?
No no it shouldn't. hmm
weird.. ya I'm stumped :c darn.

Answer 51

It's fine. Thanks again for helping me zep! I'm gonna move onto some chemistry work to give whatever part of my brain that does algebra a break. :P

Answer 52

hah k \c:/ good work!