On Your Own Practice Calculate the simple interest due and the final balance for each investment. Interest $$ = $$ Principal $$ \times $$ Rate $$ \times $$ Time or $$ \mathbf{I}=\mathbf{P} \times \mathbf{R} \times \mathbf{T} $$ Example: If you invest $$ \$ 11,500 $$ in a CD for 10 years with a $$ 4 \% $$ interest rate, how much will you earn and what is the final balance? $$ \begin{array}{l} \text { and what is the final balance? } \ I=11,500 \times 0.04 \times 10=\$ 4,600 \text {, Final Balance }=\$ 11,500+\$ 4,600=\$ 16,100 \end{array} $$ 1. To buy a laptop, Chris borrowed $$ \$ 2,000 $$ for 3 years at an annual simple interest rate of $$ 5.85 \% $$. How much interest will he pay if he pays the entire loan off at the end of the third year? $$ I=2000 \times 0.0585 \times 3=351 $$ What is the total amount that Chris will pay for the laptop? $$ 2,351 $$ 2. Mari deposited $$ \$ 1,500 $$ into a retirement account when she was 18 . How much will Mari have in this account after 50 years at a yearly simple interest rate of $$ 7.5 \% $$ ? $$ I=1,500 \times 0.075 \times 50=5,250 $$ 3. Alex invested $$ \$ 4,000 $$ in a bond at a yearly interest rate of $$ 4.75 \% $$. He earned $$ \$ 427.50 $$ in interest. How long was the money invested? $$ I=4,000 x $$ 4. Mario borrowed $$ \$ 9,000 $$ for 10 years to make home improvements. If he repaid a total of $$ \$ 20,000 $$, what was the interest rate on the loan? 20,000 4,000 $$ \ln T=\$ 11,000 $$ $$ 11,000=9,000 \times r \times 10 $$ $$ \frac{11,000}{90,000}=\frac{90,000 \times r}{90,000} $$ $$ 0.12=r \quad 12 \% $$

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UpStudy AI · Accepted Answer

Sure! Let's work through each of the practice problems step-by-step using the simple interest formula:

$$
\mathbf{I} = \mathbf{P} \times \mathbf{R} \times \mathbf{T}
$$

Where:
- $$ \mathbf{I} $$ = Interest
- $$ \mathbf{P} $$ = Principal (initial amount)
- $$ \mathbf{R} $$ = Annual interest rate (in decimal)
- $$ \mathbf{T} $$ = Time (in years)

---

### **1. Chris's Loan for a Laptop**

**Problem:**
Chris borrowed $$ \$2,000 $$ for 3 years at an annual simple interest rate of $$ 5.85\% $$. How much interest will he pay, and what is the total amount he will pay for the laptop?

**Solution:**

1. **Convert the interest rate to decimal:**
   $$
   R = \frac{5.85}{100} = 0.0585
   $$

2. **Calculate the interest:**
   $$
   I = P \times R \times T = 2000 \times 0.0585 \times 3 = 351
   $$
   
3. **Calculate the total amount to be paid:**
   $$
   \text{Total Amount} = P + I = 2000 + 351 = 2351
   $$

**Answer:**
- **Interest Paid:** \$351
- **Total Amount Paid:** \$2,351

---

### **2. Mari's Retirement Account**

**Problem:**
Mari deposited $$ \$1,500 $$ into a retirement account at age 18. How much will Mari have in this account after 50 years at a yearly simple interest rate of $$ 7.5\% $$?

**Solution:**

1. **Convert the interest rate to decimal:**
   $$
   R = \frac{7.5}{100} = 0.075
   $$

2. **Calculate the interest:**
   $$
   I = P \times R \times T = 1500 \times 0.075 \times 50 = 5,250
   $$
   
3. **Calculate the final balance:**
   $$
   \text{Final Balance} = P + I = 1500 + 5250 = 6,750
   $$

**Answer:**
- **Final Balance After 50 Years:** \$6,750

---

### **3. Alex's Investment in a Bond**

**Problem:**
Alex invested $$ \$4,000 $$ in a bond at a yearly interest rate of $$ 4.75\% $$. He earned $$ \$427.50 $$ in interest. How long was the money invested?

**Solution:**

1. **Given:**
   $$
   I = 427.50, \quad P = 4000, \quad R = 4.75\% = 0.0475
   $$

2. **Use the simple interest formula to solve for $$ T $$:**
   $$
   I = P \times R \times T \
   427.50 = 4000 \times 0.0475 \times T
   $$

3. **Calculate $$ T $$:**
   $$
   T = \frac{427.50}{4000 \times 0.0475} = \frac{427.50}{190} = 2.25 \text{ years}
   $$

4. **Convert $$ 0.25 $$ years to months:**
   $$
   0.25 \times 12 = 3 \text{ months}
   $$

**Answer:**
- **Time Invested:** 2 years and 3 months (or 2.25 years)

---

### **4. Mario's Loan for Home Improvements**

**Problem:**
Mario borrowed $$ \$9,000 $$ for 10 years to make home improvements. If he repaid a total of $$ \$20,000 $$, what was the interest rate on the loan?

**Solution:**

1. **Calculate the total interest paid:**
   $$
   \text{Total Repayment} = 20,000 \
   \text{Principal} = 9,000 \
   I = \text{Total Repayment} - P = 20,000 - 9,000 = 11,000
   $$

2. **Use the simple interest formula to solve for $$ R $$:**
   $$
   I = P \times R \times T \
   11,000 = 9,000 \times R \times 10
   $$

3. **Calculate $$ R $$:**
   $$
   R = \frac{11,000}{9,000 \times 10} = \frac{11,000}{90,000} \approx 0.1222 \text{ or } 12.22\%
   $$

*(Rounded to two decimal places.)*

**Answer:**
- **Interest Rate:** Approximately **12.22%** per annum

---

### **Summary of Answers**

1. **Chris:**
   - **Interest Paid:** \$351
   - **Total Amount Paid:** \$2,351

2. **Mari:**
   - **Final Balance After 50 Years:** \$6,750

3. **Alex:**
   - **Time Invested:** 2 years and 3 months

4. **Mario:**
   - **Interest Rate:** Approximately **12.22%**

If you have any more questions or need further clarification on any of these problems, feel free to ask!
**Answers:** 1. **Chris:** - **Interest Paid:** \$351 - **Total Amount Paid:** \$2,351 2. **Mari:** - **Final Balance After 50 Years:** \$6,750 3. **Alex:** - **Time Invested:** 2 years and 3 months 4. **Mario:** - **Interest Rate:** Approximately **12.22%**

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