To calculate the amount in the account after 10 years, we'll use the compound interest formula:

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

Where:

• $A$ is the amount in the account after interest.
• $P$ is the principal (initial deposit), which is $5000.
• $r$ is the annual interest rate, which is 3% (or 0.03 as a decimal).
• $n$ is the number of times interest is compounded per year, which is 12 (monthly compounding).
• $t$ is the number of years the money is invested, which is 10 years.

Now, plug in the values:

$A = 5000 \left( 1 + \frac{0.03}{12} \right)^{12 \times 10}$

Let's calculate this:

$A = 5000 \left( 1 + 0.0025 \right)^{120}$

$A = 5000 \left( 1.0025 \right)^{120}$

$A = 5000 \times 1.34935 \approx 6746.75$

So, after 10 years, you will have approximately $6,746.75 in the account.

Would you like a more detailed explanation, or do you have any questions?

Related Questions:

1. What would the balance be after 5 years?
2. How does the compounding frequency affect the final amount?
3. What would the final amount be if the interest rate were 5% instead of 3%?
4. How can I calculate the interest earned after 10 years?
5. If I increase my deposit to $10,000, what will my balance be after 10 years?

Tip:

For faster calculations, using a financial calculator or an online compound interest calculator can save you time on similar problems.