a. Use the appropriate formula to determine the periodic deposit.
b. How much of the financial goal comes from deposits and how much comes from​ interest?
Periodic Deposit
Rate
Time
Financial Goal
​$? at the end of each year
7​% compounded annually
14 years
​$120 comma 000
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Part 1
a. The periodic deposit is ​$

enter your response here.
​(Do not round until the final answer. Then round up to the nearest dollar as​ needed.)
Part 2
b. ​$

enter your response here of the ​$120 comma 000 comes from deposits and ​$

enter your response here comes from interest.
​(Use the answer from part​ (a) to find these answers. Round to the nearest dollar as​ needed.)

To solve this problem, we need to find the periodic deposit amount (denoted as $ P $) that will grow to a financial goal of $120,000 in 14 years, given an interest rate of 7% compounded annually.

### Part 1: Determine the Periodic Deposit
We use the **Future Value of an Annuity formula**:

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

Where:
- $ FV $ is the future value (the financial goal), $120,000.
- $ P $ is the periodic deposit (which we need to find).
- $ r $ is the interest rate per period (annual rate of 7%, or 0.07).
- $ n $ is the number of periods (14 years).

Rearrange the formula to solve for $ P $:

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

Now plug in the values:

\[
P = \frac{120{,}000 \times 0.07}{(1 + 0.07)^{14} - 1}
\]

Let's calculate this.

\[
P = \frac{120{,}000 \times 0.07}{(1.07)^{14} - 1}
\]

First, calculate $ (1.07)^{14} $:

\[
(1.07)^{14} \approx 2.5023
\]

Now, subtract 1 from that value:

\[
2.5023 - 1 = 1.5023
\]

Then multiply the future value by the interest rate:

\[
120{,}000 \times 0.07 = 8{,}400
\]

Finally, divide:

\[
P \approx \frac{8{,}400}{1.5023} \approx 5{,}592.88
\]

Rounding up to the nearest dollar:

\[
P = \$5{,}593
\]

### Part 2: Determine the Contribution from Deposits and Interest
First, calculate the total amount of deposits made:

\[
\text{Total Deposits} = P \times n = 5{,}593 \times 14 = 78{,}302
\]

Next, find the amount that comes from interest by subtracting the total deposits from the financial goal:

\[
\text{Interest Earned} = 120{,}000 - 78{,}302 = 41{,}698
\]

### Final Answers:
a. The periodic deposit is **$5,593**.

b. **$78,302** of the $120,000 comes from deposits, and **$41,698** comes from interest.

Would you like more details or have any further questions? Here are some related questions:

1. How does the number of periods affect the periodic deposit required to reach a financial goal?
2. What would be the impact of increasing the interest rate on the periodic deposit?
3. How does the future value change if the interest is compounded semi-annually instead of annually?
4. How would the periodic deposit change if the financial goal were $150,000 instead of $120,000?
5. Can you calculate the interest earned if the deposit amount is increased by $500 annually?
6. What would the periodic deposit be if the goal was to reach $120,000 in only 10 years?
7. How does the frequency of compounding affect the total interest earned?
8. What if the interest rate drops to 5%? How would that impact the periodic deposit?

**Tip:** Always double-check your formula inputs and rounding steps to ensure accuracy in financial calculations.

Learn how to calculate the periodic deposit and interest contributions to achieve a financial goal of $120,000 in 14 years with a 7% annual compound interest rate. Includes step-by-step solution using the Future Value of an Annuity formula.

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