Final answer:
The question involves calculating the present value and the accumulated amount of a continuous flow of money at a constant rate, given an annual interest rate compounded continuously over a specific period.
Step-by-step explanation:
The question pertains to the calculation of present value and future or accumulated amount of a constant money flow when compounded continuously at a given interest rate.
(A) To calculate the present value (PV) of a future sum of money, we can use the formula:
PV = F / e^(rt)
Where:
- F is the future payment
- e is the base of the natural logarithm (approximately 2.71828)
- r is the annual interest rate (as a decimal)
- t is the time in years
Since the flow of money is continuous, to find the present value of the money flow at t=10 years and r=5%, we would calculate the present value of each potential future payment of $900 and then sum them up over the 10 years.
(B) To find the accumulated amount at t=10 years, we use the formula for continuous compounding:
A = Pe^(rt)
Where:
- A is the accumulated amount
- P is the principal amount (in this case, the rate of flow of money = $900 per year)
- r is the annual interest rate (as a decimal)
- t is the time in years
So, the accumulated amount of money flow at t=10, with a rate of 5% compounded continuously, would be:
A = 900e^(0.05*10)
It is important to integrate the flow of money over the period to find the total value.