Question

You start to save for a car and invest $2,000 that earns 2.4% interest compounded annually. How many years will it take to have $5,000?

Answer 1

\[2000(1.024)^t=5000\] solve for \(t\)

Answer 2

any ideas on how to do it?

Answer 3

Yes thank you so much.

Answer 4

let me know what you get if you want me to check it
you can almost write the answer without work
it is
\[x=\frac{\ln(2.5)}{\ln(1.024)}\]

Answer 5

Wait I actually completely forgot how to solve for t....

Answer 6

1) divide by \(2000\) to get
\[(1.024)^t=2.5\]

Answer 7

Oh and then after do I divide by 1.024?

Answer 8

2) use the change of base formula to get
\[t=\frac{\ln(2.5)}{\ln(1.024)}\]

Answer 9

Is the answer 2.4?

Answer 10

seems very unlikely you will invest $2000 at a measly 2.4% interest and get two and half times you money in only 2.4 years
i 'd be rich by now

Answer 11

Oh oops.... Im so confused. I divided 2.5 by 1.024 and got 2.44140625

Answer 12

more like 38 or 39 years
they will have floating google cars by then
http://www.wolframalpha.com/input/?i=log%282.5%29%2Flog%281.024%29

Answer 13

How did you get 38 or 39?

Answer 14

calculator
only way to do it
look at the link i sent

Answer 15

I know but I divided the 2 numbers and I didn't get that