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

Answer:

73 years

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:

$(1+r)^t=\frac{A}{P}\\t=log_{1+r}(\frac{A}{P})=log_{1+0.055}(\frac{100,000}{2000})=73$

So, it will take 73 years.