Final answer:
The present value of a continuous stream of payments at a continuously compounding interest rate is calculated using the continuous annuity formula, considering the payment value, interest rate, and time frame.
Step-by-step explanation:
The student is asking about the present value of a continuous stream of payments at a continuously compounding interest rate, which is a concept in financial mathematics. To calculate the present value of a continuous payment stream, you use the formula for the present value of an annuity when the compounding is continuous. For a continuous stream of payments, the present value (PV) is given by the formula:
PV = P * (1 - e-rt)/r
where P is the payment per period, r is the interest rate, t is the number of years, and e is the base of the natural logarithm. In this case, P is $150,750, r is 5.9% or 0.059, and t is 5 years.
Calculating the present value for a continuous annuity:
PV = $150,750 * (1 - e-0.059*5)/0.059
After plugging in the values and doing the calculation, the present value would give us the worth of the continuous payment stream today considering the specified interest rate and time frame. Remember, the provided interest rate in the question was 5.9%, and not 15% as in the reference information.
It is important to mention that to find the entire present value, you would need to calculate the present value for each payment at each point in time and then sum those values up. However, in the case of continuous payments, this is simplified by the continuous annuity formula provided.