Questions: The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Principal Rate Compounded Time 5000 2% annually 2 years A. Find how much money there will be in the account after the given number of years. B. Find the interest earned.

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Principal Rate Compounded Time 5000 2% annually 2 years A. Find how much money there will be in the account after the given number of years. B. Find the interest earned.
Transcript text: The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. \begin{tabular}{|c|c|c|c|} \hline Principal & Rate & Compounded & Time \\ \hline$\$ 5000$ & $2 \%$ & annually & 2 years \\ \hline \end{tabular} A. Find how much money there will be in the account after the given number of years. B. Find the interest earned.
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Solution

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Solution Steps

Step 1: Convert the annual interest rate from a percentage to a decimal

To convert the annual interest rate to a decimal, divide the rate by 100. Thus, \(r = 2 / 100 = 0.02\).

Step 2: Identify the number of times the interest is compounded per year

The interest is compounded \(m = 1\) times per year.

Step 3: Determine the number of years the money is invested

The money is invested for \(n = 2\) years.

Step 4: Use the compound interest formula to calculate the future value

Using the formula \(A = P(1 + \frac{r}{m})^{mn}\), where \(P = 5000\), \(r = 0.02\), \(m = 1\), and \(n = 2\), we find that the future value \(A\) is approximately \(A = 5202\).

Step 5: Calculate the interest earned

The interest earned over the period is \(A - P = 202\).

Final Answer: The future value of the investment is approximately 5202 and the interest earned is approximately 202.

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