To solve this problem, we need to use the formula for compound interest which is A = P(1 + r/n)^(nt). In our situation, the interest is compounded annually, so n equals 1 and our formula simplifies to A = P(1 + r)^t.
Let's substitute the given values into our formula:
- A (the final amount) is $43,000.
- P (the principal amount) is $25,000.
- r (the annual interest rate) is 8%, we convert this to decimal form by dividing by 100, so r becomes 0.08.
We want to find t (the time in years the money is invested for).
Our equation now looks like this: 43000 = 25000(1 + 0.08)^t. We want to isolate t, so let's rearrange our equation:
t = log(43000 / 25000) / log(1 + 0.08).
Now, we just need to solve this equation. Using a calculator, we find:
t = log(1.72) / log(1.08)
t ~ 7.046737970528499.
Thus, it would take approximately 7 years for James' account to reach $43,000.