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To solve this, we need to use the formula for the future value of a series of periodic payments, compounded annually. This formula is given by:

\[
FV = P \times \frac{(1 + r)^t - 1}{r}
\]

Where:
- $FV$ is the future value or financial goal (which is $160,000).
- $P$ is the periodic deposit we are trying to find.
- $r$ is the annual interest rate (6% or 0.06).
- $t$ is the number of periods (14 years).

We can rearrange this formula to solve for $P$ (the periodic deposit):

\[
P = \frac{FV \times r}{(1 + r)^t - 1}
\]

### Step 1: Calculate the periodic deposit ($P$).

Let me compute this value.The periodic deposit needed to reach a financial goal of $160,000 over 14 years, with an interest rate of 6% compounded annually, is approximately **$7,613.59**.

### Step 2: Break down the contributions of deposits and interest.

Now, we will calculate how much of the financial goal comes from direct deposits and how much comes from interest.

The total amount deposited over 14 years is simply the periodic deposit multiplied by the number of periods:

\[
\text{Total Deposits} = P \times t
\]

The interest earned is then the difference between the final financial goal and the total deposits:

\[
\text{Interest Earned} = FV - \text{Total Deposits}
\]

Let me compute both values.The breakdown of the financial goal is as follows:
- **Total Deposits**: $106,590.20
- **Interest Earned**: $53,409.80

This means that out of the $160,000 financial goal, approximately $106,590.20 comes from the direct deposits, and $53,409.80 comes from interest.

Would you like further details or clarifications on any part of the solution?

Here are 5 related questions for further exploration:
1. How does the future value change if the interest rate is increased to 7%?
2. What would the periodic deposit be for a financial goal of $200,000 over 10 years at 5% interest?
3. How much more interest is earned if the time is extended to 20 years?
4. What is the effect of changing the compounding frequency to quarterly instead of annually?
5. How does inflation impact the real value of the financial goal over time?

**Tip**: Always ensure the interest rate matches the compounding period. If compounding occurs more frequently than annually, the rate and periods should be adjusted accordingly.

What is the periodic deposit required to reach a financial goal of $160,000 in 14 years at 6% interest compounded annually, and how much comes from deposits versus interest?

Learn how to calculate the periodic deposit required to reach a financial goal of $160,000 in 14 years, with 6% interest compounded annually. This problem involves compound interest formulas and series of periodic payments. Breakdown includes how much comes from deposits and interest.

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