Use the TI 84 finance section of a calc to plug in numbers

Find the time for an account earning interest at the annual rate of 4% (compounded annually) to grow from $2000 to $3600. (Round your answer to the nearest year.) years

To find the time it takes for an account to grow from $2000 to $3600 at an annual interest rate of 4%, compounded annually, using the TVM (Time Value of Money) solver on a TI-84 calculator, follow these steps:

### Step-by-Step Process on TI-84:

1. **Press [APPS]** to open the application menu.
2. **Select "Finance"** and then choose `1:TVM Solver`.
3. You will see the following variables:
   - `N` (number of periods)
   - `I%` (interest rate per year)
   - `PV` (present value)
   - `PMT` (payment each period)
   - `FV` (future value)
   - `P/Y` (payments per year)
   - `C/Y` (compounds per year)

### Input the following values:

- **`N`**: Leave this blank; it's the value you're solving for.
- **`I%`**: Enter `4` (since the annual interest rate is 4%).
- **`PV`**: Enter `-2000` (negative because it's the present investment).
- **`PMT`**: Enter `0` (there are no additional payments).
- **`FV`**: Enter `3600` (future value you want the investment to grow to).
- **`P/Y` and `C/Y`**: Both set to `1` (compounded annually).

4. **Press [ALPHA] then [ENTER]** to solve for `N`.

### Calculation:

The value of `N` (time in years) should come out to approximately **12.96**, which rounds to **13 years**.

### Answer:
It will take about **13 years** for the account to grow from $2000 to $3600 at a 4% annual interest rate, compounded annually.

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Would you like more details or have any other questions? Here are 5 related questions:

1. How do you adjust this process if the interest is compounded monthly?
2. What is the formula for compound interest, and how does it relate to this?
3. What happens if there are regular payments made into the account?
4. How would changing the interest rate affect the time to reach the future value?
5. Can you calculate the final amount after a fixed time if the interest rate changes?

**Tip:** Always remember to input the present value as a negative number in the TVM Solver because it's an outflow (an investment).

Find the time for an account earning interest at the annual rate of 4% (compounded annually) to grow from $2000 to $3600. (Round your answer to the nearest year.)

Learn how to calculate the time it takes for an account to grow from $2000 to $3600 at an annual interest rate of 4%, compounded annually. This problem covers key concepts such as compound interest and exponential growth, with a step-by-step guide on using the TI-84 calculator. Suitable for Grades 9-12.

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