Andrew deposits $1104.18
 each quarter into an annuity account for his child's college fund in order to accumulate a future value of $95,000
 in 16
 years. How much of the $95,000
 will Andrew ultimately deposit in the account, and how much is interest earned? Round your answers to the nearest cent, if necessary.

Formulas



To solve this problem, we can break it down into two parts: calculating how much Andrew will deposit over the 16 years and determining how much of the future value is from interest earned. We'll also use the formula for the future value of an annuity to check if Andrew will reach his target of $95,000 in 16 years.

### Formulas
1. **Future Value of an Annuity (FVA)**:
   \[
   FVA = P \times \frac{(1 + r)^n - 1}{r}
   \]
   where:
   - $ FVA $ = future value of the annuity (which is $95,000 in this case),
   - $ P $ = regular deposit per period ($1104.18),
   - $ r $ = interest rate per period (which we will need to know),
   - $ n $ = total number of periods (16 years, quarterly deposits).

2. **Total Deposits**:
   \[
   \text{Total Deposits} = P \times n
   \]
   (since deposits are made regularly).

3. **Interest Earned**:
   \[
   \text{Interest Earned} = \text{Future Value} - \text{Total Deposits}
   \]

### Part 1: Total Amount Deposited
We can calculate the total amount Andrew deposits over the 16 years.

1. Since Andrew deposits $1104.18 every quarter, the total number of deposits is:
   \[
   n = 16 \text{ years} \times 4 \text{ quarters per year} = 64 \text{ quarters}
   \]

2. The total amount deposited is:
   \[
   \text{Total Deposits} = 1104.18 \times 64 = 70667.52
   \]

### Part 2: Interest Earned
Andrew's target future value is $95,000. To find the interest earned, we subtract the total deposits from the future value:
\[
\text{Interest Earned} = 95000 - 70667.52 = 24332.48
\]

### Final Answers:
- Total amount deposited: **$70,667.52**
- Interest earned: **$24,332.48**

Would you like further details or clarifications? 

Here are five related questions for practice:
1. What is the future value of an annuity if Andrew deposits $1100 instead?
2. How much would Andrew need to deposit each quarter to reach a future value of $100,000?
3. How would a higher interest rate affect the total interest earned?
4. What is the future value if Andrew only deposits for 10 years but wants the same final amount?
5. How much would Andrew have if he stopped depositing after 10 years but left the money to accumulate for the remaining 6 years?

**Tip**: When dealing with annuities, the interest rate per period is critical for accurately calculating the future value!

Andrew deposits $1104.18 each quarter into an annuity account for his child's college fund in order to accumulate a future value of $95,000 in 16 years. How much of the $95,000 will Andrew ultimately deposit in the account, and how much is interest earned? Round your answers to the nearest cent, if necessary.

Learn how Andrew deposits $1104.18 quarterly to accumulate $95,000 in 16 years for his child's college fund. Explore annuity formulas, including the future value and interest earned. Suitable for students in Grades 11-12.

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