QuestionDecember 16, 2025

(Suggested time for completion: 7 minutes) Given an annual interest rate of 9.0% compute the future value of an ordinary annuity cash flow of 2,000 per year for forty years. For TVM excel file, click here If instead the PV tables are preferred, click here.

(Suggested time for completion: 7 minutes) Given an annual interest rate of 9.0% compute the future value of an ordinary annuity cash flow of 2,000 per year for forty years. For TVM excel file, click here If instead the PV tables are preferred, click here.
(Suggested time for completion: 7 minutes) Given an annual interest rate of 9.0% 
compute the future value of an ordinary annuity cash flow of 2,000 per year for
forty years. For TVM excel file, click here If instead the PV tables are preferred, click
here.

Solution
4.4(325 votes)

Answer

6,957,651.20 Explanation 1. Identify the formula for the future value of an ordinary annuity The formula is: **FV = P \times \frac{( (1 + r)^n - 1)}{r}**, where P = payment per year, r = interest rate per year, n = number of years. 2. Assign values P = 2000, r = 0.09, n = 40. 3. Compute growth factor (1 + r)^n = (1.09)^{40} \approx 314.0943. 4. Subtract 1 314.0943 - 1 = 313.0943. 5. Divide by r \frac{313.0943}{0.09} \approx 3478.8256. 6. Multiply by payment FV = 2000 \times 3478.8256 \approx 6,957,651.20.

Explanation

1. Identify the formula for the future value of an ordinary annuity <br /> The formula is: **$FV = P \times \frac{( (1 + r)^n - 1)}{r}$**, where $P$ = payment per year, $r$ = interest rate per year, $n$ = number of years. <br /><br />2. Assign values <br /> $P = 2000$, $r = 0.09$, $n = 40$. <br /><br />3. Compute growth factor <br /> $(1 + r)^n = (1.09)^{40} \approx 314.0943$. <br /><br />4. Subtract 1 <br /> $314.0943 - 1 = 313.0943$. <br /><br />5. Divide by $r$ <br /> $\frac{313.0943}{0.09} \approx 3478.8256$. <br /><br />6. Multiply by payment <br /> $FV = 2000 \times 3478.8256 \approx 6,957,651.20$.
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