Questions: Jim deposited 54000 into an account with 2.4% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 4 years?

Solution Steps

To solve this problem, we need to use the formula for compound interest. The formula is:

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

where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (initial deposit).
• \( r \) is the annual interest rate (decimal).
• \( n \) is, you know, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, the,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,To solve this problem, we need to use the formula for compound interest. The formula is:

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

where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (initial deposit).
• \( r \) is the annual interest rate (decimal).
• \( n \) is the number of times that interest is compounded per year.
• \( t \) is the time the money is invested for in years.

In this case, \( P = 54000 \), \( r = 0.024 \), \( n = 12 \) (since the interest is compounded monthly), and \( t = 4 \).

We are given the following values for the compound interest calculation:

• Principal amount \( P = 54000 \)
• Annual interest rate \( r = 0.024 \)
• Number of times interest is compounded per year \( n = 12 \)
• Time in years \( t = 4 \)

We use the compound interest formula:

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

Substituting the given values into the formula:

\[ A = 54000 \left(1 + \frac{0.024}{12}\right)^{12 \times 4} \]

Calculating the expression:

\[ A = 54000 \left(1 + 0.002\right)^{48} = 54000 \left(1.002\right)^{48} \]

This results in:

\[ A \approx 59435.29099090584 \]

Rounding to the nearest cent gives:

\[ A_{\text{rounded}} = 59435.29 \]

Final Answer