This problem involves compound interest growth, and we can solve it using the compound interest formula:

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

Where:

• $A$ is the final amount in the account ($36,700),
• $P$ is the initial principal amount ($3,500),
• $r$ is the annual interest rate (8.75% = 0.0875),
• $t$ is the time in years (what we need to find),
• $n$ is the number of times the interest is compounded per year (if not mentioned, we assume it's compounded annually, so $n = 1$).

Since we are not given any information about compounding more frequently, we'll assume it is compounded annually ($n = 1$). Therefore, the formula simplifies to:

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

Now, substituting the known values:

$36,700 = 3,500(1 + 0.0875)^t$

We can solve for $t$, the time in years. I'll calculate it now.It will take 28.0 years for the account value to reach $36,700 with an annual interest rate of 8.75%.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this concept:

1. What would the time be if the interest was compounded monthly instead of annually?
2. How much interest will be earned over these 28 years?
3. What would the final amount be if the interest rate was 10% instead?
4. How long would it take if the initial deposit was $5,000 instead of $3,500?
5. What happens to the time if the interest rate decreases to 5%?

Tip: The frequency of compounding can have a significant impact on the final amount in an investment. Consider compounding quarterly or monthly for more growth!