Find the accumulated future value of a 11 -year $\$ 90,000$ continuous income stream that has been compounded continuously at $3.5 \%$. Round to the nearest dollar.
Answer
Final Answer: The accumulated future value of a 11 -year $90,000 continuous income stream that has been compounded continuously at 3.5% is \(\boxed{132265}\).
Step 1 ：We are given a continuous income stream of $90,000 for 11 years, compounded continuously at an annual interest rate of 3.5%. We are asked to find the accumulated future value of this income stream.
Step 2 ：The future value of a continuous income stream can be calculated using the formula: \(FV = P * e^{rt}\), where: \(FV\) is the future value, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal form), \(t\) is the time in years, and \(e\) is the base of the natural logarithm, approximately equal to 2.71828.
Step 3 ：Substituting the given values into the formula, we get: \(FV = 90000 * e^{(0.035 * 11)}\).
Step 4 ：Solving the above expression, we find that the future value of the income stream is approximately $132,265.
Step 5 ：Final Answer: The accumulated future value of a 11 -year $90,000 continuous income stream that has been compounded continuously at 3.5% is \(\boxed{132265}\).
