Bill deposits $100 to his savings account biweekly. His savings account pays a nominal interest rate of 5% per year, compounded every six months. What is his savings account's effective interest rate for a 6-month period?

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The effective interest rate for a 6-month period can be calculated using the formula for converting a nominal annual rate to an effective rate for a given compounding period: $ (1 + \frac{r}{n})^n - 1 $, where $ r $ is the nominal annual rate and $ n $ is the number of compounding periods per year. Given a nominal annual rate of 5% (or 0.05) and compounding every six months (n = 2), the effective 6-month interest rate is $ (1 + \frac{0.05}{2})^2 - 1 = (1.025)^2 - 1 = 1.050625 - 1 = 0.050625 $ or 5.0625% annually. To find the semi-annual (6-month) effective rate, we simply use the given nominal rate divided by the number of compounding periods, which is $ \frac{0.05}{2} = 0.025 $ or 2.5%.

Bill Deposits $100 to His Savings Account Biweekly