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.)
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.)
Solution
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 \(\text{18825}\).