Question

The income from an established chain of laundromats is a continuous stream with its annual rate of flow at time t given by

f(t) = 120,000 (dollars per year).

If money is worth 3% compounded continuously, find the present value and future value of this chain over the next 5 years. (Round your answers to the nearest dollar.)

	present value	$
	future value	$

Answer 1

a). Calculating the Present value of theses Cash flows using compounded continously formula:-

$Present Value = P*(\frac{1-e^{-rt}}{e^r-1})$

where, P = Periodic Cash Flow = $120,000

r = Interest rate = 0.03

n = no of years = 5

$Present Value = 120,000*(\frac{1-e^{(-0.03*5)}}{e^{0.03}-1})$

1 -el-0.15) PresentValue = 120,000 * 0.03 – 1

$Present Value = 120,000*(\frac{1-0.86070797642506}{1.0304545339535-1})$

Present Value = $548,852.36

b). Calculating the Future Value of theses Cash flows using compounded continously formula:-

$Future Value = P*(\frac{e^{rt}-1}{e^r-1})$

where, P = Periodic Cash Flow = $120,000

r = Interest rate = 0.03

n = no of years = 5

$Present Value = 120,000*(\frac{e^{(0.03*5)}-1}{e^{0.03}-1})$

$Present Value = 120,000*(\frac{e^{(0.15)}-1}{e^{0.03}-1})$

$Present Value = 120,000*(\frac{1.1618342427283 -1}{1.0304545339535-1})$

Present Value = $637,675.47