using a TI BA II Plus Calculator Olivia plans to contribute $800.00 at the start of every 3 months to an investment that earns 8.75% compounded quarterly. If Olivia starts contributing on her 29th birthday, how much will she accumulate by her 44th birthday? Assume she doesn't make a contribution on her 44th birthday.
Future Value: 
 


To solve this problem using a **TI BA II Plus** calculator, we need to apply the formula for the **future value of an ordinary annuity** since Olivia is making contributions at regular intervals (every 3 months) into an account that earns interest compounded quarterly.

### Variables:
- **PMT (Payment):** 800 (since she contributes $800 at the start of every quarter)
- **Interest Rate (I/Y):** 8.75% annually, compounded quarterly.
- **Number of Periods (N):** The number of quarters between her 29th and 44th birthdays.
- **Future Value (FV):** This is what we are solving for.

### Steps to Solve:

1. **Identify the number of quarters:**
   - Olivia is contributing from her 29th birthday until her 44th birthday. This is 15 years.
   - Since contributions are made quarterly, there are 4 quarters per year.
   - $ N = 15 \text{ years} \times 4 \text{ quarters per year} = 60 \text{ quarters} $

2. **Set the interest rate per period (I/Y):**
   - The annual interest rate is 8.75%, but it’s compounded quarterly, so the interest rate per quarter is:
   - $ I/Y = \frac{8.75\%}{4} = 2.1875\% \text{ per quarter} $

3. **Set PMT:**
   - Olivia contributes $800 at the start of each quarter. Since it's an annuity due (payments made at the start of each period), we need to set the calculator to this mode.

4. **PV (Present Value):**
   - Olivia is not starting with any initial amount, so the present value is 0.

5. **FV:**
   - We will calculate this.

### Calculator Settings:
1. Set the calculator to **BGN (beginning)** mode because the payments are made at the start of the period.
   - Press `2nd` → `BGN` → `2nd` → `SET` to switch to **Begin** mode.
   
2. Input the following values into the calculator:
   - **N = 60** (number of quarters)
   - **I/Y = 2.1875** (quarterly interest rate)
   - **PMT = -800** (the payment is outflow, hence negative)
   - **PV = 0** (no initial investment)

3. Compute the **future value**:
   - Press `CPT` → `FV`.

Let's calculate this.The future value of Olivia's investment by her 44th birthday, given her quarterly contributions of $800 and an interest rate of 8.75% compounded quarterly, will be approximately **$99,529.43**.

### Would you like further details or have any questions?

Here are five related questions you could explore:
1. How would the future value change if Olivia contributed monthly instead of quarterly?
2. What if the interest rate increased to 10% annually—how much would she accumulate?
3. How much would Olivia need to contribute quarterly to reach $120,000 by her 44th birthday?
4. What is the total amount of interest earned over the 15 years?
5. How would the future value change if contributions were made at the end of each period instead?

**Tip:** Always ensure you are in the correct mode (Begin/End) on your financial calculator, as it affects how payments are treated!

Olivia plans to contribute $800.00 at the start of every 3 months to an investment that earns 8.75% compounded quarterly. If Olivia starts contributing on her 29th birthday, how much will she accumulate by her 44th birthday? Assume she doesn't make a contribution on her 44th birthday.

Learn how to calculate the future value of an annuity due with quarterly contributions of $800 at an interest rate of 8.75% compounded quarterly. This detailed solution explains the time value of money, annuity due, and future value formula. Suitable for advanced high school or college-level finance students.

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