Final answer:
The capital gain of the TIPS in percentage terms is calculated by determining the percentage change in CPI and applying it to the par value of the bond. Based on the given CPI values and a par value of $1,000, the capital gain is approximately 5.16%, which is answer (a).
Step-by-step explanation:
The capital gain on a 2.75 percent Treasury Inflation-Protected Securities (TIPS) can be calculated based on the Consumer Price Index (CPI) adjustment from the beginning to the end of the year. With an issue CPI reference of 184.60, a starting annual CPI of 191.70, and an ending annual CPI of 201.60, we can determine the change in principal due to inflation. The principal adjustment for TIPS is calculated as the ending CPI divided by the issue CPI, multiplied by the par value.
Therefore, the adjusted principal value at the end of the year would be ($1,000 * 201.60 / 184.60) which equals $1,091.98. To find the capital gain, we subtract the initial principal value of $1,000 from the adjusted principal value at year-end, resulting in a gain of $91.98. The capital gain in percentage terms is then ($91.98 / $1,000) * 100%, which equals 9.20% (when not rounded to two decimal places). However, the exact percentage increase in CPI from beginning to end of the year is (201.60 / 191.70) - 1 = 0.0517 or 5.17%. This implies that the capital value of the bond would have increased by 5.17% simply due to inflation adjustments. Given the answer choices and instructions to not round intermediate steps and round the final answer to two decimal places, the closest correct choice is 5.16% percent, answer (a).