Questions: a. Use the appropriate formula to find the value of the annuity. b. Find the interest. Periodic Deposit Rate Time 1000 at the end of each year 6.5% compounded annually 20 years (i) Click the icon to view some finance formulas. a. The value of the annuity is . (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is . (Use the answer from part (a) to find this answer. Round to the nearest dollar as needed.)

a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.

Periodic Deposit  Rate  Time
1000 at the end of each year  6.5% compounded annually  20 years

(i) Click the icon to view some finance formulas.
a. The value of the annuity is  .
(Do not round until the final answer. Then round to the nearest dollar as needed.)
b. The interest is  .
(Use the answer from part (a) to find this answer. Round to the nearest dollar as needed.)
Transcript text: a. Use the appropriate formula to find the value of the annuity. b. Find the interest. \begin{tabular}{|l|l|l|} \hline Periodic Deposit & Rate & Time \\ \hline$\$ 1000$ at the end of each year & $6.5 \%$ compounded annually & 20 years \\ \hline \end{tabular} (i) Click the icon to view some finance formulas. a. The value of the annuity is $\$$ $\square$ . (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is $\$$ $\square$ (Use the answer from part (a) to find this answer. Round to the nearest dollar as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Future Value of the Annuity (FVA)

To calculate the future value of an annuity, we use the formula: \[FVA = PMT \times \left(\frac{(1 + \frac{r}{n})^{n \times t} - 1}{\frac{r}{n}}\right)\] Substituting the given values: \(PMT = 1000\), \(r = 0.065\), \(n = 1\), and \(t = 20\), we get: \[FVA = 1000 \times \left(\frac{(1 + \frac{0.065}{1})^{20} - 1}{\frac{0.065}{1}}\right) = 38825\]

Step 2: Calculate the Total Interest Earned

The total amount of deposits is calculated as: \(Total Deposits = PMT \times n \times t = 20000\). Thus, the total interest earned is: \(Total Interest = FVA - Total Deposits = 38825 - 20000 = 18825\).

Final Answer

The future value of the annuity is \(\text{38825}\) and the total interest earned is \(\text{18825}\).

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