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 PV ) = \$4300
  • Interest Rate (r r ) = 838%=67800 8 \frac{3}{8} \% = \frac{67}{800}
  • Time (t t ) = 214 2 \frac{1}{4} years = 94 \frac{9}{4}
Step 2: Convert Interest Rate to Decimal

Convert the interest rate from a percentage to a decimal: r=67800=0.08375 r = \frac{67}{800} = 0.08375

Step 3: Calculate Future Value

Using the formula for future value: FV=PV×(1+r)t FV = PV \times (1 + r)^t Substituting the values: FV=4300×(1+0.08375)94 FV = 4300 \times (1 + 0.08375)^{\frac{9}{4}} Calculating this gives: FV≈5152.99 FV \approx 5152.99

Final Answer

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

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