To calculate the future value of an annuity with biannual payments at an annual interest rate of 5%, you need to adjust the annual interest rate to reflect the biannual compounding.
The formula to convert an annual interest rate to a rate per period is:
\[ r = \frac{\text{annual interest rate}}{\text{number of periods per year}} \]
In this case, the annual interest rate is 5% or 0.05, and since the payments are made biannually (2 times a year), we have:
\[ r = \frac{0.05}{2} = 0.025 \]
Thus, the value of \( r \) that must be substituted into the formula to calculate the future value of the annuity is:
0.025
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