Find the present and future values of a constant income stream of $6700 per year over an 8-year period at an interest rate of 4.75% compounded continuously. Round your answers to the nearest cent.
a) Find the present value of the income stream. Present Value =
b) Find the future value of the income stream. Future Value =
c) How much of the future value is from interest? Answer =
To find the present and future values of a constant income stream, we can use the formula for calculating present value and future value with continuous compounding.
The present value (PV) of a continuous income stream can be calculated using the formula:
PV = Income / e^(r*t)
where:
Income = annual income
e = Euler's number ≈ 2.71828
r = interest rate (in decimal form)
t = number of years
a) Find the present value of the income stream:
PV = $6700 / e^(0.0475*8)
To calculate this, type "6700 / (2.71828^(0.0475*8))" into a calculator or use a spreadsheet software like Excel.
b) Find the future value of the income stream:
The future value (FV) of a continuous income stream over time can be calculated using the formula:
FV = PV * e^(r*t)
where PV is the present value calculated in part a.
FV = PV * e^(0.0475*8)
To calculate this, multiply the present value (from part a) by e raised to the power of (interest rate * number of years).
c) How much of the future value is from interest:
The interest part of the future value can be calculated by subtracting the present value from the future value:
Interest = FV - PV
To calculate this, subtract the present value (from part a) from the future value (from part b).
Remember to round your answers to the nearest cent as specified.