1. **State the problem:** Walter deposits 697.20 each quarter into an annuity to accumulate 65000 in 17 years. We need to find the total amount deposited and the interest earned.
2. **Formula for future value of an ordinary annuity:**
$$FV = P \times \frac{(1 + r)^n - 1}{r}$$
where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments.
3. **Identify variables:**
- $P = 697.20$
- $FV = 65000$
- Number of years = 17
- Payments per year = 4 (quarterly)
- Total payments $n = 17 \times 4 = 68$
4. **Find the quarterly interest rate $r$:**
Rearranging the formula to solve for $r$ is complex and typically requires trial, error, or financial calculator. Since $r$ is not given, we cannot find it directly here. However, the problem only asks for total deposits and interest earned, so we can calculate total deposits as:
5. **Calculate total amount deposited:**
$$\text{Total deposits} = P \times n = 697.20 \times 68 = 47409.60$$
6. **Calculate interest earned:**
$$\text{Interest} = FV - \text{Total deposits} = 65000 - 47409.60 = 17590.40$$
**Final answers:**
- Total amount deposited: 47409.60
- Interest earned: 17590.40
Annuity Deposits D386F5
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.