Question

if Alexis invest $2,000 into a fund that earns 5.5% interest compounded annually, how long will it take for her investment to grow into $100,000?

Answer 1

73 years

Step-by-step explanation:

To solve this problem, we can use the formula for the annual compound interest, which is:

`A=P(1+r)^t`

where:

A is the final amount after time t

P is the principal

r is the rate of interest

t is the time

In this problem, we have:

`P=\$2000` is the principal

`r=0.055` is the interest rate (5.5%)

We want to find the time t at which the amount of money is

A = $100,000

Therefore, we can re-arrange the equation and solve for t:

`(1+r)^t=(A)/(P)\\t=log_(1+r)((A)/(P))=log_(1+0.055)((100,000)/(2000))=73`

So, it will take 73 years.