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 month
7.25​% compounded monthly
40 years
​$1 comma 000 comma 000
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Part 1
a. The periodic deposit is ​$
  
356.
​(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 ​$1 comma 000 comma 000 comes from deposits and ​$
  
enter your response here comes from interest.
​(Use the answer from part​ (a) to find these answers. Round to the nearest dollar as​ needed.)

### Part 1: Determine the periodic deposit using the future value of an ordinary annuity formula

The formula to calculate the future value $ FV $ of an ordinary annuity (for periodic deposits) is:

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

Where:
- $ FV $ = future value ($1,000,000)
- $ P $ = periodic deposit (which we are solving for)
- $ r $ = monthly interest rate (annual interest rate divided by 12)
- $ n $ = total number of deposits (number of months)

Given:
- Annual interest rate = 7.25% = 0.0725
- Compounded monthly, so monthly interest rate $ r = \frac{0.0725}{12} = 0.00604167 $
- Time period = 40 years = 480 months
- Future value $ FV = 1,000,000 $

Now, solve for the periodic deposit $ P $:

\[
1,000,000 = P \times \frac{(1 + 0.00604167)^{480} - 1}{0.00604167}
\]

First, let's calculate the value of the fraction on the right-hand side.

### Part 2: How much comes from deposits and how much from interest

Once we know the periodic deposit $ P $, we can calculate the total amount deposited and the total interest earned over 40 years.

- Total amount from deposits = $ P \times n $ (total number of deposits)
- Total interest = Future value - Total amount from deposits

Let me calculate these values.### Part 1: Periodic Deposit
The periodic deposit is approximately $ P = 356 $ (rounded up to the nearest dollar).

### Part 2: Breakdown of the Financial Goal
- Total amount from deposits: $ 170,425 $ (rounded to the nearest dollar)
- Total interest earned: $ 829,575 $ (rounded to the nearest dollar)

Thus, of the $1,000,000 financial goal:
- $170,425 comes from the deposits.
- $829,575 comes from the interest.

Would you like further details or explanations? 

Here are five related questions:
1. How does compound interest impact savings over time?
2. What if the interest rate changes—how does it affect periodic deposits?
3. What is the formula for compound interest, and how is it different from simple interest?
4. How would the periodic deposit change if the goal were reached in 30 years instead of 40?
5. What are the advantages of monthly deposits versus yearly ones?

**Tip**: Consistency in deposits over time significantly amplifies gains due to compound interest, especially with monthly compounding!

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 month 7.25% compounded monthly 40 years $1,000,000

Learn how to calculate the periodic deposit required to reach a financial goal of $1,000,000 over 40 years with a 7.25% interest rate compounded monthly. Understand the breakdown of the contribution from deposits and the amount of interest earned.

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