Reuben deposited $2000

into an account with a 3.8% annual interest rate, compounded semiannually. Assuming that no withdrawals are made, how long will it take for the investment to grow to
$3000?

I don't know if he does algebra, but look for Yay Math videos on U tube. He saved me in Geometry last year. He could be a little annoying, but he is a great teacher. Hope this helps.

If x is the number of years, you need

(1 + .038/2)^(2x) = 3000/2000

To determine how long it will take for the investment to grow to $3000, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (in this case, $3000)
P = the principal amount (in this case, $2000)
r = the annual interest rate (in this case, 3.8% or 0.038)
n = the number of times interest is compounded per year (in this case, semiannually, so it would be 2)
t = the number of years

Now, let's substitute the given values into the formula:

$3000 = $2000(1 + 0.038/2)^(2t)

Next, we can simplify the equation:

1.5 = (1.019)^2t

To solve for t, we need to isolate the exponent:

Taking the natural logarithm of both sides:

ln(1.5) = 2t ln(1.019)

Now, we can solve for t by dividing both sides by (2 ln(1.019)):

t = ln(1.5) / (2 ln(1.019))

Using a calculator or a math software, we can compute the value of t.