Answer: 3.5%

## Explanation For a zero-coupon bond, the price is calculated as: \[ P = \frac{F}{(1 + \frac{r}{m})^{m \times n}} \] Where: - \( P \) = price = 90 - \( F \) = face value = 100 (assumed for zero-coupon bonds) - \( r \) = annual yield-to-maturity (what we're solving for) - \( m \) = compounding frequency = 4 (quarterly compounding) - \( n \) = years to maturity = 3 Rearranging the formula: \[ 90 = \frac{100}{(1 + \frac{r}{4})^{4 \times 3}} \] \[ 90 = \frac{100}{(1 + \frac{r}{4})^{12}} \] \[ (1 + \frac{r}{4})^{12} = \frac{100}{90} = 1.111111 \] \[ 1 + \frac{r}{4} = (1.111111)^{\frac{1}{12}} \] \[ 1 + \frac{r}{4} = 1.008797 \] \[ \frac{r}{4} = 0.008797 \] \[ r = 0.035188 \] \[ r = 3.52\% \] This is closest to 3.5% (Option C). **Verification:** \[ (1 + \frac{0.035}{4})^{12} = (1.00875)^{12} = 1.1100 \] \[ \frac{100}{1.1100} = 90.09 \approx 90 \] Therefore, the correct answer is **C. 3.5%**.

Author: LeetQuiz .