To calculate the future value of an investment with compound interest, we use the compound interest formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (initial investment), which is $2900.
• $r$ is the annual interest rate (in decimal form), so $3.5\% = 0.035$.
• $n$ is the number of times the interest is compounded per year (monthly compounding means $n = 12$).
• $t$ is the number of years the money is invested (50 years).

Now, substitute the values into the formula:

$A = 2900 \left(1 + \frac{0.035}{12}\right)^{12 \times 50}$

Let's compute this step by step.

The investment would be worth $16,645.89 after 50 years.

Would you like further details or have any questions about the calculation?

Here are 5 related questions for practice:

1. What would the investment be worth after 40 years?
2. How much interest would you have earned after 50 years?
3. How would the result change if the interest rate were 4% instead of 3.5%?
4. How long would it take for the investment to double in value?
5. What if the interest was compounded quarterly instead of monthly?

Tip: The more frequently interest is compounded, the more rapidly the investment grows.