To calculate the amount of money in the account after 8 years, we can use the formula for compound interest:

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

Where:

• $A$ = the amount of money in the account after interest
• $P$ = the principal amount (initial investment)
• $r$ = annual interest rate (decimal form)
• $n$ = number of times the interest is compounded per year
• $t$ = time the money is invested or borrowed for, in years

Given:

• $P = 2,800$
• $r = 6.2\% = 0.062$
• $n = 12$ (since the interest is compounded monthly)
• $t = 8$ years

Now, plug these values into the formula:

$A = 2800 \left( 1 + \frac{0.062}{12} \right)^{12 \times 8}$

Let's compute this:

$A = 2800 \left( 1 + 0.0051667 \right)^{96}$ $A = 2800 \left( 1.0051667 \right)^{96}$ $A = 2800 \times 1.747422051$ $A \approx 4,894.79$

Thus, the amount in the account after 8 years is approximately $4,890 (to the nearest ten dollars).

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Would you like more details on how this formula works or have any questions? Here are some additional questions that could help:

1. How would the outcome change if the interest rate were different?
2. How does the frequency of compounding (e.g., quarterly vs. monthly) impact the final amount?
3. What is the effect of making additional deposits during the investment period?
4. How does compound interest compare to simple interest over the same time period?
5. How can you calculate the time it takes for an investment to double with compound interest?

Tip: When working with compound interest, increasing the frequency of compounding (e.g., monthly or daily) slightly increases the final amount.