Find the approximate (with an integral estimate) present and future values of a constant income stream of 2500 dollars per year over a period of 40 years, assume a 5 percent annual interest rate compounded continuously. Find current and future value?
To find the approximate present and future values of a constant income stream, we can use the concept of present value and future value with continuous compounding.
First, let's find the present value of the income stream. The present value (PV) formula for continuous compounding is given by:
PV = future value / e^(rt)
Where:
PV is the present value
future value is the future value of the income stream
e is Euler's number (approximately 2.71828)
r is the interest rate (5% or 0.05 in decimal form)
t is the time period (40 years)
Using the formula, we can calculate the present value:
PV = 2500 / e^(0.05*40)
Now, let's find the future value of the income stream. The future value (FV) formula for continuous compounding is given by:
FV = present value * e^(rt)
Using the formula, we can calculate the future value:
FV = PV * e^(0.05*40)
Now, let's perform the calculations:
PV = 2500 / e^(0.05*40) ≈ 2500 / 2.71828^(0.05*40) ≈ 2500 / 2.71828^2 ≈ 2500 / 7.389 ≈ 338.31 dollars
FV = PV * e^(0.05*40) ≈ 338.31 * 2.71828^(0.05*40) ≈ 338.31 * 2.71828^2 ≈ 338.31 * 7.389 ≈ 2500 dollars
Therefore, the approximate present value of the constant income stream is around 338.31 dollars, and the approximate future value of the income stream is around 2500 dollars.