To calculate the balance in the account after 18 years with monthly compounding, we will use the compound interest formula:

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

Where:

• $A$ is the balance in the account after interest.
• $P$ is the principal amount (initial investment), which is $5000.
• $r$ is the annual interest rate (APR), which is 3% or 0.03.
• $n$ is the number of times the interest is compounded per year. Since it's compounded monthly, $n = 12$.
• $t$ is the time in years, which is 18 years.

Step 1: Plug in the values

$A = 5000 \left(1 + \frac{0.03}{12}\right)^{12 \times 18}$

Step 2: Simplify the expression

$A = 5000 \left(1 + 0.0025\right)^{216}$ $A = 5000 \left(1.0025\right)^{216}$

Step 3: Calculate $(1.0025)^{216}$

Using a calculator: $(1.0025)^{216} \approx 1.693$

Step 4: Multiply by the principal

$A = 5000 \times 1.693$ $A \approx 8465.00$

Final Answer:

The balance in the account after 18 years is approximately $8,465.00.

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Would you like more details or clarification on any step?

Here are 5 related questions:

1. How does increasing the interest rate affect the final balance?
2. What would the balance be if compounding was done annually instead of monthly?
3. How would the balance change if the investment period was only 10 years?
4. How does the frequency of compounding (monthly vs yearly) affect the total return?
5. How would the result change if you were to invest a larger initial amount?

Tip: The more frequently the interest is compounded, the greater the final amount due to the compounding effect.