   Chapter 8.4, Problem 16E

Chapter
Section
Textbook Problem

The present value of an income stream is the amount that would need to be invested now to match the future value as described in Exercise 15 and is given by ∫ 0 T f ( t ) e − r t d t . Find the present value of the income stream in Exercise 15.

To determine

To calculate: The present value of the income.

Explanation

Given information:

The function of future value of the income is 0Tf(t)erTdt.

The rate for received income is f(t)=8,000e0.04t.

Interest rate (r) is 6.2%=0.062.

Time T is measured in years and f(t) is measured in dollars per year.

Calculation:

Show the present value as follows:

0Tf(t)ertdt (1)

Substitute 6 years for T, 0.062 for r, and 8,000e0.04t for f(t) in Equation (1).

0Tf(t)ertdt=068,000e0.04te0.062tdt=8,00006(e0.04te0.062t)dt=8,00006(e0

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