Questions: Given the rate per compounding period, find r, the annual rate. 5.3% per half-year

Solution Steps

To convert the rate per compounding period \(r_p = 5.3\%\) to a decimal, we divide by 100: \[r_p = \frac{5.3}100 = 0.053\]

Using the formula \[ r = (1 + \frac{r_p}{100})^n - 1 \], we substitute \(r_p\) and \(n\): \[ r = (1 + 0.053)^2 - 1 = 0.109\]

To convert \(r\) from a decimal to a percentage, we multiply by 100: \[ r = 0.109 \times 100 = 10.88\%\]

Final Answer: The annual rate \(r\) is 10.88\%.