A principal of $3000 earns 9% per year simple interest. How long will it take for the future value to become $3459? (Round your answer to two decimal places.)
years
what do I enter in the finance tab of a ti-84 calc

To solve this problem, we can use the formula for simple interest:

\[ A = P + P \cdot r \cdot t \]

Where:
- $ A $ is the future value.
- $ P $ is the principal amount.
- $ r $ is the annual interest rate (in decimal form).
- $ t $ is the time in years.

Given:
- $ P = 3000 $
- $ r = 0.09 $ (9% per year)
- $ A = 3459 $

We need to find $ t $. First, rearrange the formula to solve for $ t $:

\[ A = P + P \cdot r \cdot t \]

Subtract $ P $ from both sides:

\[ A - P = P \cdot r \cdot t \]

Divide both sides by $ P \cdot r $:

\[ t = \frac{A - P}{P \cdot r} \]

Now plug in the values:

\[ t = \frac{3459 - 3000}{3000 \cdot 0.09} \]

Calculate the numerator and the denominator:

\[ t = \frac{459}{270} \]

\[ t = 1.7 \]

So, it will take approximately 1.70 years for the future value to become $3459.

### Entering the information in a TI-84 calculator:

1. Press the `APPS` button.
2. Select `Finance` by pressing `1`.
3. Select `TVM Solver` by pressing `1`.

Enter the following values:
- `N` = 1.70 (This represents the time in years, which we have calculated.)
- `I%` = 9 (The annual interest rate.)
- `PV` = -3000 (The principal amount, entered as a negative value because it is an outflow.)
- `PMT` = 0 (Since there are no additional payments.)
- `FV` = 3459 (The future value.)
- `P/Y` = 1 (Payments per year, which is 1 in this case for annual interest.)
- `C/Y` = 1 (Compounding periods per year, which is also 1 for simple interest.)

After entering these values, you can solve for `N` by moving the cursor next to `N` and pressing `ALPHA` followed by `ENTER`. This should confirm the time in years.

Would you like further details or have any questions?

Here are five related questions you might find interesting:
1. How would the time change if the interest rate were increased to 12% per year?
2. What would be the future value if the time were extended to 3 years?
3. How much interest is earned after 1.70 years?
4. What would be the required principal to achieve a future value of $4000 in 1.70 years at 9% interest?
5. How would the calculation change if the interest were compounded annually instead of being simple interest?

**Tip:** When using the TI-84 calculator for financial calculations, always double-check that you have entered all values correctly and that your settings (e.g., compounding periods) match the problem requirements.

A principal of $3000 earns 9% per year simple interest. How long will it take for the future value to become $3459? (Round your answer to two decimal places.)

Find out how long it will take for a $3000 principal to grow to $3459 with a 9% simple interest rate. This detailed step-by-step solution covers financial mathematics and algebraic concepts, perfect for high school students (Grades 9-12).

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