Find the amount needed to deposit into an account today that will yield a typical pension payment of $30,000 at the end of each of the next 16 years for the given annual interest rate. (Round your answer to the nearest cent.)

4.9%

$
using finance part of calc in ti84 plug numbers in for me

To find the amount to deposit today (present value) that will allow you to withdraw $30,000 at the end of each year for the next 16 years, given a 4.9% annual interest rate, we can use the **Present Value of an Annuity** formula. 

The formula is:

\[
PV = P \times \left(1 - \left(1 + r\right)^{-n}\right) \div r
\]

Where:
- $PV$ = present value (the amount to deposit today)
- $P$ = payment amount ($30,000)
- $r$ = interest rate per period (4.9% or 0.049)
- $n$ = number of periods (16 years)

### Steps to enter this in the TI-84:

1. **Go to the TVM Solver** by pressing `2nd` and then `FINANCE` (this is above the key for `x^-1`).
2. Select **TVM Solver** from the menu.
3. Plug in the following values:
   - **N = 16** (for the 16 years)
   - **I% = 4.9** (for the 4.9% interest rate)
   - **PMT = -30,000** (negative because it’s an outgoing payment)
   - **FV = 0** (since no money is left at the end)
   - **P/Y = 1** (payments per year)
   - **C/Y = 1** (compounding frequency per year)
4. Move the cursor to **PV** and press **Alpha** + **Enter** to compute the present value.

After computing this, you should get the result for how much you need to deposit today. Let me calculate the result for you as well.

The amount needed to deposit today is approximately **$327,459.73**.

Would you like more details or have any questions on how this was calculated?

Here are 5 related questions for further practice:
1. How would the present value change if the interest rate was 6% instead of 4.9%?
2. What happens to the amount needed if the payments are made monthly instead of yearly?
3. If the payments were to continue for 20 years instead of 16, what would the present value be?
4. How would the present value be affected if you withdrew $40,000 each year instead of $30,000?
5. How much interest will be earned in total by the end of the 16-year period?

**Tip:** Increasing the number of periods or the interest rate generally reduces the amount needed to deposit upfront, as more time or higher interest allows for more growth.

Find the amount needed to deposit into an account today that will yield a typical pension payment of $30,000 at the end of each of the next 16 years for the given annual interest rate. (Round your answer to the nearest cent.) 4.9% $ using finance part of calc in ti84 plug numbers in for me

Calculate the present value of an annuity where $30,000 is withdrawn annually for 16 years with a 4.9% interest rate. Learn how to use the TI-84 calculator to solve this financial problem with step-by-step guidance. Perfect for college-level financial mathematics.

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