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From the sample answer to answer this question y is it divde

From the images, the problem involves Zal needing to save for a trip. The table provides future values of an annuity of $1 over different periods of years, depending on various interest rates, with the goal of determining how much Zal needs to deposit annually over 4 years at a 3% interest rate compounded annually to reach his goal of $15,000.

### Step-by-Step Explanation:

1. **Future Value of Annuity (FVA)**: The table shows the future value of $1 at different interest rates and periods. The value corresponding to 4 years and a 3% interest rate is **4.184**.
   
2. **Total Savings Required**: Zal needs to save $15,000 in total.

3. **How Annuities Work**: The future value of annuity (FVA) formula helps determine how much annual payments (deposits) you need to reach a certain future value. The formula is:
   \[
   \text{Future Value} = P \times FVA
   \]
   where:
   - $ P $ is the annual payment (deposit),
   - $ FVA $ is the future value of the annuity.

4. **Solving for the Annual Payment**:
   \[
   15000 = P \times 4.184
   \]
   To find the annual payment $ P $, divide both sides by 4.184:
   \[
   P = \frac{15000}{4.184} = 3585.09
   \]

### Why Divide?

The reason for dividing is that the table value (4.184) represents the **total effect** of the annuity compounding over 4 years at a 3% rate. Since the total future value ($15,000) is already known, you divide it by this factor to find how much needs to be deposited each year.

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Would you like further details on the calculation or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the formula for the future value of an annuity with regular deposits?
2. How does changing the interest rate affect the required annual deposit?
3. How would the calculation change if the compounding period was different (e.g., monthly)?
4. Can the future value of an annuity formula be used for varying annual deposits?
5. What happens if Zal starts saving after the first year, instead of from the beginning?

**Tip**: Always check if the interest rate is compounded annually, monthly, or in some other way. This can change the formula and the future value considerably.

From the sample answer to answer this question y is it divide

Learn how to calculate annual deposits needed to save $15,000 in 4 years at a 3% interest rate compounded annually. This problem covers future value of annuities and compound interest, suitable for students in Grades 11-12.

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