Let's break down the problem step by step: ### 1. **Stated interest rate:** 7.00% per year, **compounded quarterly** ### 2. **Find the interest rate per period (month)** #### Step 1: Find the **quarterly** rate - Stated annual interest rate (nominal): \( r = 7\% = 0.07 \) - Quarterly rate: \( r_q = \frac{0.07}{4} = 0.0175 \) per quarter #### Step 2: Find the **effective annual rate (EAR)** \[ \text{EAR} = (1 + r_q)^4 - 1 = (1 + 0.0175)^4 - 1 \] \[ (1.0175)^4 = 1.071361 \] \[ \text{EAR} = 1.071361 - 1 = 0.071361 \] \[ \text{EAR} = 7.1361\% \] #### Step 3: Find the **monthly rate** (\( r_m \)) that gives the EAR \[ (1 + r_m)^{12} = 1 + \text{EAR} \] \[ (1 + r_m)^{12} = 1.071361 \] \[ 1 + r_m = (1.071361)^{1/12} \] \[ 1 + r_m = 1.005755 \] \[ r_m = 0.005755 \] ### **Final Answer** \[ \boxed{0.005755} \] **The monthly interest rate is:** **0.5755%** (rounded to four decimal places) **0.005755** (as a decimal, rounded to six decimal places) --- **To six decimal places:** **Monthly interest rate = 0.005755**