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\%.