New parents wish to save for their newborn's education and wish to have $39,000 at the end of 17 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 4.9% compounded annually? (Round your answers to two decimal places.)
$
1,522.48

Correct: Your answer is correct.

How much interest would they earn over the life of the account?
$
13117.84

Correct: Your answer is correct.

Determine the value of the fund after 11 years.
$
How do I plug this last part into a finance ti-84 part of a calculator

To determine the value of the fund after 11 years using a financial calculator like the TI-84, you're solving for the **future value** (FV) of the account after 11 years of regular annual payments.

Here's how you can plug the values into the TVM (Time Value of Money) Solver on your TI-84 calculator:

### Step-by-step Instructions:

1. **Access the TVM Solver:**
   - Press the `APPS` button on your TI-84 calculator.
   - Select `Finance` (usually option 1).
   - Then select `TVM Solver` (usually option 1 again).

2. **Enter the Known Values:**
   - **N**: The number of years the parents have been saving so far is 11. Since the deposits are made at the end of each year, set $ N = 11 $ (this represents the number of payment periods).
   - **I%**: The annual interest rate is 4.9%. So, enter $ I\% = 4.9 $.
   - **PV**: The present value (initial investment) is zero because they're starting from nothing. So, $ PV = 0 $.
   - **PMT**: The payment amount is the annual contribution the parents are making. In this case, it's \$1,522.48. So, enter $ PMT = -1522.48 $ (negative because it's a payment going out).
   - **FV**: Leave this value blank (you are solving for this).
   - **P/Y**: This represents the number of payments per year. Since they are contributing annually, set $ P/Y = 1 $.
   - **C/Y**: This represents the number of compounding periods per year. Since the interest is compounded annually, set $ C/Y = 1 $.
   - **PMT: END**: Ensure that `PMT` is set to `END`, because the payments are made at the end of each year.

3. **Solve for FV:**
   - Once you've entered all the values, scroll down to `FV`, then press `ALPHA` followed by `ENTER` to calculate the future value of the fund after 11 years.

This will give you the value of the fund after 11 years based on the regular contributions and the annual interest rate of 4.9%.

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### Additional Information:
The formula for calculating the future value of an annuity can also be written as:
\[
FV = PMT \times \frac{{(1 + r)^N - 1}}{r}
\]
Where:
- $ PMT $ = 1,522.48 (annual payment)
- $ r $ = 0.049 (annual interest rate)
- $ N $ = 11 (number of years)

Would you like me to go over the manual calculation using this formula?

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### Follow-up Questions:
1. How does the formula change if the interest is compounded monthly instead of annually?
2. What would be the value of the fund after 17 years with the same conditions?
3. What if the parents decided to contribute for 15 years instead of 17, how would the value differ?
4. How does compounding affect the amount of interest earned?
5. What would be the impact on the total savings if they increase their annual contribution by 5% every year?

---

### Tip:
Always make sure you input negative values for payments and positive values for deposits into the TI-84 TVM Solver to avoid calculation errors.

New parents wish to save for their newborn's education and wish to have $39,000 at the end of 17 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 4.9% compounded annually? (Round your answers to two decimal places.)

Discover how much parents need to save annually to reach a $39,000 goal for their newborn's education in 17 years. Learn how to calculate the future value of an annuity with a 4.9% interest rate compounded annually. Suitable for Grades 10-12 and finance enthusiasts.

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