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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Present Value In Exercises 67-72, find the present value of the income c (in dollars) over t 1 years at the given annual inflation rate r. See Examples 6 and 7.

c = 5000 + 25 t e t / 10 ,   r = 6 % ,   t 1 = 10  years

To determine

To calculate: The present value if the income c in dollar is c=5000+25tet/10 over the time interval of 10 years and the inflation rate is r=6%.

Explanation

Given information:

The income is c=5000+25tet/10 the provided time interval is t1=10 years and the inflation rate is r=6%.

Formula used:

Present value can be calculated as:

Present value=0t1c(t)ertdt

Integration by parts:

udv=uvvdu

Common integration using integration by parts

xneaxdx

Where u=xn and dv=eaxdx

Calculation:

Consider the income function is c=5000+25tet/10

It is provided that t1=10 years and the inflation rate is r=6%.

The provided rate r=6% which can also be written as;

r=6%=6100=0.06

Now find Present value with the help of the formula: Present value=0t1c(t)ertdt

Substitute the value of t1=10, r=0.06 and c=5000+25tet/10 in the above function.

0t1c(t)ertdt=010(5000+25tet/10)e0.06tdt=010(5000e0.06t)dt+01025te0

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