Question

Help please :c
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.

I started with 10,000=39145(1+.03/12)^12t
I ended up with in(10000/39145)/12in(1.0025) =t
My only problem is I keep getting t=0.021235284081 for an answer which I believe is wrong.

Answer 1

@ganeshie8 Any ideas?

Answer 2

@phi Help?

Answer 3

Did I get the function wrong when I was isolating t?

Answer 4

you should get
\[ \frac{10000}{39145} = 1.0025^{12 t } \]
\[ \ln\left( \frac{10000}{39145} \right) = 12 \ln(1.0025) t \]
\[ \frac{ \ln\left( \frac{10000}{39145} \right)}{12 \ln(1.0025)} = t \]

Answer 5

ln means "natural log" . You could also use log (base 10)

you will get a negative number.

Answer 6

That exactly what I have then I solved it using Mathway and t=0.021235284081 is what I get, I'm just no so confident in myself that it's right.

Answer 7

So I'd re-do the problem but change where "in" is to "log(10)"?

Answer 8

You should get a negative number, not 0.0212
do you have a calculator?

or use google:
log(10000/39145)=
to get the top number

Answer 9

okay let me solve it one sec

Answer 10

I got -0.5926762974

Answer 11

now find
12*log(1.0025)

Answer 12

I got 0.0130125755

Answer 13

So would I divide them both together?

Answer 14

yes, now do
-0.5926762974/0.0130125755

Answer 15

type into google
-0.5926762974 / 0.0130125755 =

Answer 16

I got -45.5464252561

Answer 17

So that's my answer?

Answer 18

yes, -45.55 months, or -46 months rounded

Answer 19

Thank you so much man!!

Answer 20

yw