Problem

Find the future value for the annuity due with the given rate. Payments of $\$ 900$ for 7 years at $0.29 \%$ compounded semiannually The future value of the annuity due is $\$ \square$. (Do not round until the final answer. Then round to the nearest cent as needed.)

Solution

Step 1 :Given that the payments per period (P) is $900, the annual interest rate (r) is 0.29% or 0.0029, the number of times that interest is compounded per period (n) is 2 (since it's compounded semiannually), and the time the money is invested for in years (t) is 7.

Step 2 :We can calculate the future value of the annuity due using the formula: \(FV = P \times \left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right] \div \left(\frac{r}{n}\right) \times \left(1 + \frac{r}{n}\right)\)

Step 3 :Substituting the given values into the formula, we get: \(FV = 900 \times \left[\left(1 + \frac{0.0029}{2}\right)^{2 \times 7} - 1\right] \div \left(\frac{0.0029}{2}\right) \times \left(1 + \frac{0.0029}{2}\right)\)

Step 4 :Solving the above expression, we find that the future value of the annuity due is approximately $12737.89.

Step 5 :Final Answer: The future value of the annuity due is \(\boxed{12737.89}\)

From Solvely APP
Source: https://solvelyapp.com/problems/36063/

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