Questions: A couple deposits 19,000 into an account earning 5% annual interest for 30 years. Calculate the future value of the investment if the interest is compounded semiannually. Round your answer to the nearest cent.

A couple deposits 19,000 into an account earning 5% annual interest for 30 years. Calculate the future value of the investment if the interest is compounded semiannually. Round your answer to the nearest cent.
Transcript text: A couple deposits $\$ 19,000$ into an account earning $5 \%$ annual interest for 30 years. Calculate the future value of the investment if the interest is compounded semiannually, Round your answer to the nearest cent.
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Solution

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Solution Steps

Step 1: Convert the Annual Interest Rate to a Decimal

The annual interest rate is given as 5%. To convert it to a decimal, we divide by 100. Thus, \(r = 5 / 100 = 0.05\).

Step 2: Identify the Compounding Frequency

The compounding frequency (\(n\)) is given as 2 times per year.

Step 3: Use the Future Value Formula

Substitute the values into the future value formula: \[ FV = 19000 \left(1 + \frac{0.05}{2}\right)^{2*30} \]

Step 4: Calculate the Future Value

By substituting the values into the formula, we get \[ FV = 83596.01 \] after rounding to 2 decimal places.

Final Answer:

The future value of the investment, rounded to 2 decimal places, is $83596.01.

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