Final answer:
The present value of the investment generating a continuous income of $200,000/year for 6 years at a continuous interest rate of 6% is calculated using the present value formula for continuously compounded annuities, rounding the result to the nearest whole number.
Step-by-step explanation:
To find the present value of an investment generating income at the rate of R(t)=200,000 dollars/year for the next 6 years with a 6% interest rate compounded continuously, we use the formula for present value of a continuously compounded annuity:
PV = R × ¶(¶(1 - e-rt) / r)
Where R is the payment rate, r is the continual interest rate, and t is the time in years. Plugging in the values:
PV = 200,000 × ¶(¶(1 - e-0.06×6) / 0.06)
After calculating the above expression, we round to the nearest whole number to find the present value of the investment.
This is analogous to evaluating the present value of a bond that has a series of future payments discounted back to their value today using a specific discount rate. Just like with the bond example where we calculate the present discount value (PDV) of payments at different times, we sum the present values of each payment to arrive at the total present value of the investment.