Questions: Find the future value using the following data. Present Value Interest Rate Time Future Value -------------------------------------------------- 4300 8 3/8 % 2 1/4 years The future value is . (Round to the nearest cent as needed.)

Find the future value using the following data. Present Value Interest Rate Time Future Value -------------------------------------------------- 4300 8 3/8 % 2 1/4 years The future value is . (Round to the nearest cent as needed.)
Transcript text: Find the future value using the following data. \begin{tabular}{|c|c|c|c|} \hline \begin{tabular}{c} Present \\ Value \end{tabular} & \begin{tabular}{c} Interest \\ Rate \end{tabular} & Time & \begin{tabular}{c} Future \\ Value \end{tabular} \\ \hline$\$ 4300$ & $8 \frac{3}{8} \%$ & $2 \frac{1}{4}$ years & \\ \hline \end{tabular} The future value is $\$$ $\square$ (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Identify Given Values

We are given the following values:

  • Present Value (\( PV \)) = \$4300
  • Interest Rate (\( r \)) = \( 8 \frac{3}{8} \% = \frac{67}{800} \)
  • Time (\( t \)) = \( 2 \frac{1}{4} \) years = \( \frac{9}{4} \)
Step 2: Convert Interest Rate to Decimal

Convert the interest rate from a percentage to a decimal: \[ r = \frac{67}{800} = 0.08375 \]

Step 3: Calculate Future Value

Using the formula for future value: \[ FV = PV \times (1 + r)^t \] Substituting the values: \[ FV = 4300 \times (1 + 0.08375)^{\frac{9}{4}} \] Calculating this gives: \[ FV \approx 5152.99 \]

Final Answer

The future value is approximately \(\boxed{FV = 5152.99}\).

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