## Step-by-Step Solution calculate the **net income** and the **efficiency ratio** for the bank. --- ### 1. **Net Income Calculation** #### **Step 1: Calculate Net Interest Income** \[ \text{Net Interest Income} = \text{Total interest income} - \text{Total interest expense} \] \[ = 180,000 - 80,000 = 100,000 \] #### **Step 2: Calculate Net Operating Income** \[ \text{Net Operating Income} = \text{Net Interest Income} + \text{Non-interest income} + \text{Gain on securities} - \text{Non-interest expense} - \text{Provision for loan losses} \] \[ = 100,000 + 10,000 + 2,500 - 7,000 - 3,400 \] \[ = 112,500 - 7,000 - 3,400 \] \[ = 112,500 - 10,400 = 102,100 \] #### **Step 3: Subtract Taxes to get Net Income** \[ \text{Net Income} = \text{Net Operating Income} - \text{Taxes} \] \[ = 102,100 - 1,800 = 100,300 \] --- ### 2. **Efficiency Ratio Calculation** The **Efficiency Ratio** is: \[ \text{Efficiency Ratio} = \frac{\text{Non-interest expense}}{\text{Net interest income} + \text{Non-interest income}} \] \[ = \frac{7,000}{100,000 + 10,000} \] \[ = \frac{7,000}{110,000} \] \[ = .0636 \text{ or } 6.36\% \] --- ## **Final Answers** - **Net Income:** **100,300** - **Efficiency Ratio:** **6.36%** --- **Summary Table:** | Calculation | Amount | |---------------------------|-----------| | Net Income | 100,300 | | Efficiency Ratio | 6.36% |