Subjects finance

Annuity Deposits D386F5

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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