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Let's solve each of the questions step by step.

---

### **Question 15**:  
You decide to contribute to a mutual fund that averages an **8% return per year**. If you contribute **$450 monthly**:

- **How much will be in the account after 15 years?**
- **How much of this money did you deposit?**
- **How much of this money is interest earned?**

---

#### **Solution:**

1. **Monthly contribution** ($ P $) = 450 USD  
2. **Annual interest rate** ($ r $) = 8% = 0.08  
3. **Time** ($ t $) = 15 years  
4. **Number of times compounded annually** ($ n $) = 12 (since it’s compounded monthly)  

The future value of an annuity formula (regular monthly contributions with compound interest) is:

\[
A = P \times \frac{{(1 + \frac{r}{n})^{nt} - 1}}{\frac{r}{n}}
\]

Substitute the values:

\[
A = 450 \times \frac{{(1 + \frac{0.08}{12})^{12 \times 15} - 1}}{\frac{0.08}{12}}
\]

We'll calculate this value in the final step.

---

- **Amount deposited**:
\[
\text{Total deposits} = P \times n \times t
\]
\[
\text{Total deposits} = 450 \times 12 \times 15 = 81,000 \, \text{USD}
\]

- **Interest earned**:
\[
\text{Interest} = A - \text{Total deposits}
\]

---

### **Question 16**:  
You deposit **$200 each quarter** into an account earning **2.3% interest compounded quarterly**:

- **a) How much will you have in the account in 20 years?**
- **b) How much total money will you put into the account?**
- **c) How much total interest will you earn?**

---

#### **Solution**:

1. **Quarterly contribution** ($ P $) = 200 USD  
2. **Annual interest rate** ($ r $) = 2.3% = 0.023  
3. **Time** ($ t $) = 20 years  
4. **Number of times compounded annually** ($ n $) = 4 (since it’s compounded quarterly)

We use the same formula for the future value of an annuity:

\[
A = P \times \frac{{(1 + \frac{r}{n})^{nt} - 1}}{\frac{r}{n}}
\]

Substitute the values:

\[
A = 200 \times \frac{{(1 + \frac{0.023}{4})^{4 \times 20} - 1}}{\frac{0.023}{4}}
\]

We'll calculate this value at the end.

- **Amount deposited**:
\[
\text{Total deposits} = P \times n \times t
\]
\[
\text{Total deposits} = 200 \times 4 \times 20 = 16,000 \, \text{USD}
\]

- **Interest earned**:
\[
\text{Interest} = A - \text{Total deposits}
\]

---

### **Question 17**:  
You decide to contribute to a mutual fund that averages **10% return per year**. If you contribute **$125 quarterly**:

- **How much will be in the account after 10 years?**
- **How much of this money did you deposit?**
- **How much of this money is interest earned?**

---

#### **Solution**:

1. **Quarterly contribution** ($ P $) = 125 USD  
2. **Annual interest rate** ($ r $) = 10% = 0.10  
3. **Time** ($ t $) = 10 years  
4. **Number of times compounded annually** ($ n $) = 4 (since it’s compounded quarterly)

The future value formula is:

\[
A = P \times \frac{{(1 + \frac{r}{n})^{nt} - 1}}{\frac{r}{n}}
\]

Substitute the values:

\[
A = 125 \times \frac{{(1 + \frac{0.10}{4})^{4 \times 10} - 1}}{\frac{0.10}{4}}
\]

We'll calculate this value next.

- **Amount deposited**:
\[
\text{Total deposits} = P \times n \times t
\]
\[
\text{Total deposits} = 125 \times 4 \times 10 = 5,000 \, \text{USD}
\]

- **Interest earned**:
\[
\text{Interest} = A - \text{Total deposits}
\]

---

Let's now compute all the future values using the formulas mentioned.

I will calculate each of the final values.Here are the step-by-step solutions to each of the questions:

---

### **Question 15**:
- **How much will be in the account after 15 years?**  
  **Future value**: \$155,717.20  
- **How much of this money did you deposit?**  
  **Deposits**: \$81,000  
- **How much of this money is interest earned?**  
  **Interest earned**: \$74,717.20  

---

### **Question 16**:
- **a) How much will you have in the account in 20 years?**  
  **Future value**: \$20,243.08  
- **b) How much total money will you put into the account?**  
  **Deposits**: \$16,000  
- **c) How much total interest will you earn?**  
  **Interest earned**: \$4,243.08  

---

### **Question 17**:
- **How much will be in the account after 10 years?**  
  **Future value**: \$8,425.32  
- **How much of this money did you deposit?**  
  **Deposits**: \$5,000  
- **How much of this money is interest earned?**  
  **Interest earned**: \$3,425.32  

---

Would you like more detailed explanations for any of these? Here are some additional questions related to this topic:

1. How does increasing the contribution amount affect the future value?
2. What happens if the interest rate changes to 5% in question 15?
3. How do you calculate compound interest for monthly vs. quarterly contributions?
4. How can the formula be modified if the contributions are not regular?
5. How does inflation affect the real value of the future amount?

**Tip**: Regular contributions over a long period benefit greatly from compound interest—early and consistent investments can yield significant results!

You decide to contribute to a mutual fund that averages 8% return per year. If you contribute $450 monthly:
- How much will be in the account after 15 years?
- How much of this money did you deposit?
- How much of this money is interest earned?

You deposit $200 each quarter into an account earning 2.3% interest compounded quarterly:
- a) How much will you have in the account in 20 years?
- b) How much total money will you put into the account?
- c) How much total interest will you earn?

You decide to contribute to a mutual fund that averages 10% return per year. If you contribute $125 quarterly:
- How much will be in the account after 10 years?
- How much of this money did you deposit?
- How much of this money is interest earned?

Learn how to calculate compound interest for both monthly and quarterly contributions to mutual funds. Includes detailed examples with 8% and 10% annual returns. Perfect for high school students in Grades 11-12 looking to master compound interest formulas.

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