Question

Being a smart financial planner, you want to figure out how many months it will be until your principal is paid down to $10,000.00. Solve for t and show all of your work. Note that t will be negative because the number of months will decrease the principal.

Answer 1

@jim_thompson5910 @ganeshie8

Answer 2

@Hero @ParthKohli

Answer 3

@memecheaa, is that the full instructions for the question? I assume this is related to I = PRT problems.

Answer 4

Yes. it is

You are going to purchase a new car, but being a responsible consumer means doing a little bit of research first.

First, you find the vehicle you are purchasing and its price.
Vehicle: Chevy Volt
Price: $39,145

Current interest rate: 3%

Using the function A(t)=P(1+rn)nt, create the function that represents your new car loan that is compounded monthly. The principle will be the price of the vehicle you selected, not how much you are putting down.

Answer 5

Okay, there's the rest of it. Is the function \(A(t) = P(1 + rn)^{nt}\) ?
How far have you gotten with solving this?

Answer 6

@Hero: I have gotten:
A(t)=39143(1+0.03/12)^12t

Answer 7

Okay, yes, that makes more sense. The formula should be

\(A(t) = P\left(1 + \dfrac{r}{n}\right)^{nt}\)

Answer 8

Soooo
39143t=10,000(1=0.03/12)^(12t)

Answer 9

?*

Answer 10

Actually, I re-read it. It clearly says the principle should be the price of the vehicle.

Answer 11

Was i right the first time?

Answer 12

So what you had before is correct.

\(10,000 = 39143\left(1 + \dfrac{0.03}{12}\right)^{12t}\)

Answer 13

That probably explains why they said t will be negative.

Answer 14

It's not 10,000t?

Answer 15

It's definitely not 10,000t.

Answer 16

Oh.. Okay .
\[1+.0025=1.0025\] then i multiply it to 39143 right?

Answer 17

Basically, all you have to do is just solve for t.

Answer 18

But you can't multiply 39143 with 1.0025 because the 1.0025 is raised to an exponent.

Answer 19

The first step is to divide both sides by 39143

Answer 20

\(\dfrac{10,000}{39143} = \left(1.0025\right)^{12t}\)

Answer 21

Ohhhhhhhh .. now do we raise 1.0025?

Answer 22

1.0025^(12)(1)= 1.0304

Answer 23

@Hero

Answer 24

@geerky42

Answer 25

Try to take log of both sides

Answer 26

The next step is to take logs of both sides like what @geerk42 said.

Answer 27

It's probably a good idea to reduce \(\dfrac{10,000}{39143}\) before doing so.

Answer 28

@Hero thank you soooo much! :) . can you help me with one more please?

Answer 29

Post it as a new question.