rewrite and Give step-by-step solution with explanation and final answer:

---

**Problem Statement**

Damaris is a fashionista who buys only denim jackets. She deposits **\$4,000** into a savings

Question

rewrite and  Give step-by-step solution with explanation and final answer:

---

**Problem Statement**

Damaris is a fashionista who buys only denim jackets. She deposits **\$4,000** into a savings account that pays an annual nominal interest rate of **5%**. Assume this interest rate is fixed and will not change over time. On the day she makes her deposit, the price of one denim jacket is **\$100**.

1. **Initial Purchasing Power**:
   At the time of deposit, Damaris’s \$4,000 can purchase **\_\_\_\_ denim jackets**.

2. For each of the given **annual inflation rates**, determine the new price of a denim jacket after one year, assuming prices rise at the stated inflation rate. Then compute the purchasing power of Damaris’s deposit after one year in terms of denim jackets.
   Finally, calculate the **real interest rate** for each inflation rate.

Round your answers for the number of jackets **down to the nearest whole number**.
   (Example: If the fund after one year could buy 20.7 jackets, you would report **20 jackets**. If it could buy 6.9 jackets, you would report **6 jackets**.)

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### **Table to Complete**

| **Annual Inflation Rate**                                 |

VIPSolutions · Accepted Answer

Let's solve the problem step by step as requested.

---

### **Step 1: Initial Purchasing Power**

- Damaris deposits **\$4,000**.
- Price of one jacket = **\$100**.
- **Number of jackets she can buy immediately:**

$$
\text{Number of jackets} = \frac{\$4,000}{\$100} = 40
$$

---

### **Step 2: Calculations for Each Inflation Rate**

#### **Common Calculations**

- **Account balance after 1 year (with 5% interest):**

$$
\$4,000 \times (1 + 0.05) = \$4,200
$$

---

#### **A. Inflation Rate = 0%**

1. **New jacket price:**  
   $$
   \$100 \times (1 + 0) = \$100
   $$

2. **Number of jackets after 1 year:**  
   $$
   \frac{\$4,200}{\$100} = 42
   $$
   (Round down: **42 jackets**)

3. **Real interest rate:**  
   $$
   5\% - 0\% = 5\%
   $$

---

#### **B. Inflation Rate = 5%**

1. **New jacket price:**  
   $$
   \$100 \times (1 + 0.05) = \$105
   $$

2. **Number of jackets after 1 year:**  
   $$
   \frac{\$4,200}{\$105} = 40
   $$
   (Exactly **40 jackets**)

3. **Real interest rate:**  
   $$
   5\% - 5\% = 0\%
   $$

---

#### **C. Inflation Rate = 10%**

1. **New jacket price:**  
   $$
   \$100 \times (1 + 0.10) = \$110
   $$

2. **Number of jackets after 1 year:**  
   $$
   \frac{\$4,200}{\$110} = 38.18
   $$
   (Round down: **38 jackets**)

3. **Real interest rate:**  
   $$
   5\% - 10\% = -5\%
   $$

---

### **Step 3: Fill in the Table**

| **Annual Inflation Rate**                                 | **0%** | **5%** | **10%** |
| --------------------------------------------------------- | ------ | ------ | ------- |
| **Real Interest Rate**                                    | 5%     | 0%     | -5%     |
| **Number of Jackets Damaris Can Purchase after One Year** | 42     | 40     | 38      |

---

### **Final Answers**

#### 1. **Initial Purchasing Power:**
> At the time of deposit, Damaris’s \$4,000 can purchase **40 denim jackets**.

#### 2. **Table:**

| **Annual Inflation Rate**                                 | **0%** | **5%** | **10%** |
| --------------------------------------------------------- | ------ | ------ | ------- |
| **Real Interest Rate**                                    | 5%     | 0%     | -5%     |
| **Number of Jackets Damaris Can Purchase after One Year** | 42     | 40     | 38      |

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