Find the future value of the following annuity due. Assume that interest is compounded annually, there are $n$ payments of $R$ dollars, and the interest rate is $i$.
\[
R=400 ; \quad i=0.05 ; \quad n=5
\]
The future value of the annuity due is $\$ \square$.
(Round to the nearest cent as needed.)
Answer
Final Answer: The future value of the annuity due is \(\boxed{2320.77}\) dollars.
Step 1 ：We are given the following values: \(R = 400\), \(i = 0.05\), and \(n = 5\).
Step 2 ：We are asked to find the future value of the annuity due. The formula for this is: \(FV = R \times \frac{(1 + i)^n - 1}{i} \times (1 + i)\).
Step 3 ：Substituting the given values into the formula, we get: \(FV = 400 \times \frac{(1 + 0.05)^5 - 1}{0.05} \times (1 + 0.05)\).
Step 4 ：Solving the equation, we find that the future value of the annuity due is approximately \$2320.77.
Step 5 ：Final Answer: The future value of the annuity due is \(\boxed{2320.77}\) dollars.
