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Answer :
Final answer:
The present value of the income stream is approximately $904.84.
Explanation:
To find the present value of an income stream of $3000 per year for 20 years, assuming a 6% interest rate compounded continuously, we can use the formula:
PV = C / e^(r * n)
Where PV is the present value, C is the cash flow per period, r is the interest rate, and n is the number of periods.
Plugging in the given values:
PV = $3000 / e^(0.06 * 20)
Using a calculator, we can evaluate e^(0.06 * 20) to be approximately 2.71828^(1.2) = 3.32012.
Therefore, the present value is:
PV = $3000 / 3.32012 = $904.84
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The present value of the income stream is approximately $18,075.17.
To find the present value of an income stream with continuous compounding, you can use the formula for continuous compounding:
PV = FV / e^(rt)
Where:
PV = Present Value
FV = Future Value (the income stream in this case, which is $3,000 per year for 20 years)
r = Interest rate (in decimal form, so 6% becomes 0.06)
t = Time (in years)
e = Euler's number, approximately equal to 2.71828
Let's calculate it step by step:
FV = $3,000 per year for 20 years = $3,000 * 20 = $60,000
r = 6% = 0.06
t = 20 years
Now, plug these values into the formula:
PV = $60,000 / e^(0.06 * 20)
PV = $60,000 / e^(1.2)
PV ≈ $60,000 / 3.32011692 (rounded to 8 decimal places)
PV ≈ $18,075.17 (rounded to the nearest cent)
So, the present value of the income stream is approximately $18,075.17. None of the provided options matches this value. Please double-check the options or the calculation.
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