Question

Naomi invested $4,000 into a fund that is expected to grow by 5.53% per year. How long will it take the fund to be worth $8,000?

Answer 1

It will take 13.42 years.

The equation for this is in the form y=a(1+r)ˣ, where a is the initial deposit, r is the interest rate as a decimal number and x is the amount of time.  Using our information, we have the equation

8000 = 4000(1+0.053)ˣ
8000 = 4000(1.053)ˣ

Divide both sides by 4000:
8000/4000 = 4000(1.053)ˣ/4000
2 = 1.053ˣ

We will use a logarithm to solve this:
$x=\log_{1.053}2 \\ \\x=13.42$