To compute the future value of an annuity with biannual payments at an annual interest rate of 3 percent, we need to adjust the interest rate for the payment frequency.
Since the payments are made biannually, we need to determine the effective interest rate per period. The annual interest rate is 3 percent, and because there are 2 periods in a year (biannual), we divide the annual interest rate by 2.
Here's how to calculate it:
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Convert the annual interest rate to a decimal: \[ \text{Annual interest rate} = 3% = 0.03 \]
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Divide by the number of compounding periods per year (which is 2 for biannual payments): \[ r = \frac{0.03}{2} = 0.015 \]
Thus, the value of \( r \) to be used in the formula to calculate the future value of the annuity, rounded to the nearest thousandth, is:
\[ \boxed{0.015} \]
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