Question

An investor is presented with a choice of two investments: an established furniture store and a new book store. Each choice requires the same initial investment an each produces a continuous income stream of 6%, compounded continuously. The rate of flow of income from the furniture store is f(t) 12,000, and the rate of flow of income from the book store is expected to be g(t) 10,000 e.03t Compare the future values of these investments to determine which is the better choice over th next 6 years. The future value of the furniturefurniture store is $?

Answer 1

PART(a): To find the future value of the furniture store:

The rate of income flow is given by,

F(t) = 12000

The present value is given by,

PV f(t)etdt -rt

plugin the values,

(12000)e 0.06t dt PV

After integrating we get,

PV 60464.735

The future value is given by,

FV = PV.e" rt

FV 60464,735.e0.06(6)

PART(b): To find the future value of the book store:

The rate of income flow is given by,

g(t) = 10000e.03

The present value is given by,

g(t)et dt -rt PV

plugin the values,

$PV = \int_{0}^{6}(10000 e^{0.03t}) e^{-0.06t}dt$

$PV = \int_{0}^{6}(10000 e^{-0.03t}) dt$

After integrating we get,

PV =54909.93

The future value is given by,

FV = PV.e" rt

Conclusion:

The furniture store is a better choice as it has a high future value.

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