Questions: In order to pay for college, the parents of a child invest 10,000 in a bond that pays 6% interest compounded semiannually. How much money will there be in 17 years? Round your answer to the nearest cent.

In order to pay for college, the parents of a child invest 10,000 in a bond that pays 6% interest compounded semiannually. How much money will there be in 17 years? Round your answer to the nearest cent.
Transcript text: In order to pay for college, the parents of a child invest $10,000 in a bond that pays 6% interest compounded semiannually. How much money will there be in 17 years? 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 from a percentage to a decimal

To convert the annual interest rate to a decimal, divide by 100: \(r = 6 / 100 = 0.06\).

Step 2: Find the semiannual interest rate

The semiannual interest rate is obtained by dividing the annual rate by 2: \(\frac{r}{2} = 0.03\).

Step 3: Find the total number of compounding periods

Since the interest is compounded semiannually, the total number of compounding periods over \(t\) years is \(2t = 34\).

Step 4: Substitute the values into the formula to calculate the future value

Using the formula \(A = P \left(1 + \frac{r}{2}\right)^{2t}\), we find the future value: \(A = 10000 \left(1 + 0.03\right)^{34} = 27319.05\).

Final Answer:

The future value of the investment, rounded to 2 decimal places, is $27319.05.

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