Question

she invested $5000 into a fund that is expected to grow by 3.5% per year.

How long will it take the fund she invested in to be worth $10,000?

Answer 1

This is compound growth, I assume?

Answer 2

I'm assuming so , yes.

Answer 3

Do you know the formula for calculating compound growth?

Answer 4

i dont think so .

Answer 5

If we have a growth rate of \(r\) (expressed as a decimal), after 1 growth period, our initial quantity will go from \(P\) to \(P*(1+r)\).
After 2 growth periods, it will be \(P*(1+r)*(1+r) = P*(1+r)^2\)
After 3 growth periods, it will be \(P*(1+r)*(1+r)*(1+r) = P*(1+r)^3\)
After \(n\) growth periods, it will be \(P*(1+r)^n\)

Answer 6

So, what you're trying to find is the value of \(n\) such that \[10000 = 5000*(1+0.035)^n\]

Any idea how to proceed?

Answer 7

solve for n .

Answer 8

Well, yes, but do you know how to do so?

Answer 9

No .

Answer 10

First step would be to divide both sides by 5000
\[\frac{10000}{5000} = \frac{5000(1+0.035)^n}{5000}\]\[2 = (1+0.035)^n\]

Do you know about logarithms?

Answer 11

We'll use a property of logarithms that \[\log x^a = a\log x\]

then take the log of both sides:

\[\log 2 = \log (1.035)^n\]\[\log 2 = n\log 1.035\]\[n = \frac{\log 2}{\log 1.035}\]

Now you break out your calculator and compute the value of \(n\)...

Answer 12

I'll give you a hint: \(\log 2 \approx 0.30103\)

Answer 13

Not really a hint, I guess, as much as saving you a step.