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 month
5.5​% compounded monthly
12 years
​$220 comma 000
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Part 1
a. The periodic deposit is ​$

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

We can solve this problem using the **Future Value of an Annuity Formula**, which applies to periodic deposits with compound interest:

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

Where:
- $ FV $ is the future value (the financial goal, $220,000),
- $ P $ is the periodic deposit (what we are solving for),
- $ r $ is the annual interest rate (5.5% = 0.055),
- $ n $ is the number of compounding periods per year (since it's compounded monthly, $ n = 12 $),
- $ t $ is the time in years (12 years).

### Step-by-step:

1. **Substitute the known values:**
   - $ FV = 220,000 $
   - $ r = 0.055 $
   - $ n = 12 $
   - $ t = 12 $

\[
220,000 = P \times \frac{(1 + \frac{0.055}{12})^{12 \times 12} - 1}{\frac{0.055}{12}}
\]

2. **Simplify the terms inside the formula and solve for $ P $.**

Let's calculate this now.The periodic deposit required to reach the financial goal of $220,000 is approximately **$1,082** per month (rounded up to the nearest dollar).

### Part 1: The periodic deposit is **$1,082**.

Now let's move on to calculating how much of the financial goal comes from deposits and how much comes from interest. We can calculate this by determining the total amount deposited and subtracting it from the future value.

Would you like to proceed with that calculation?

Use the appropriate formula to determine the periodic deposit. How much of the financial goal comes from deposits and how much comes from​ interest? 

Periodic Deposit Rate: 5.5% compounded monthly 
Time: 12 years 
Financial Goal: $220,000.

Learn how to calculate the periodic deposit required to reach a financial goal of $220,000 over 12 years at a 5.5% interest rate compounded monthly. This problem covers key financial concepts like the future value of annuities and compound interest. Suitable for students in Grades 11-12 and college finance courses.

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