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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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College Tuition Fund Assume your grandparents had continuously invested in a college fund according to the model f ( t )   =   450 t for 18 years, at an annual interest rate of 7 % . Use the equation from Exercises 79 and 80 to answer the following. Assume the tuition cost is the same for the four years.

(a) In 2014, the tuition cost of attending The Pennsylvania State University for 1 year was estimated to be $30,452. Will the fund have grown enough to allow you to cover 4 years of tuition at The Pennsylvania State University? (Source: The Pennsylvania State University)

(b) In 2014, the tuition cost of attending The Ohio State University for 1 year was estimated to be $26,537. Will the fund have grown enough to allow you to cover 4 years of tuition at The Ohio State University? (Source: The Ohio State University)

(a)

To determine

Whether the fund is sufficient or not to cover the tuition cost after four years. If tuition cost is $30,452 for one year. If f(t)=450t for 18 years at 7% annual interest rate.

Explanation

Given information:

The provided model is f(t)=450t for 18 years at 7% and tuition cost is $30,452 for one year.

The provided equation is shown below:

Future value=ert10t1f(t)ertdt

Consider the future value from exercise 79 and 80,

Future value=ert10t1f(t)ertdt

Where r is interest rate and t1 is time period.

Here the Interest rate that is,

r=7%=0.07

The time period that is t1=18 years and model is f(t)=450t.

Now substitute all the values in the future formula as:

Future value=e(0.07)18018450te(0.07)tdt=450e(1.26)018te(0.07)tdt

Now integration with respect to t and use integration by parts as:

Let u=t and v=e(0

(b)

To determine

Whether the fund is sufficient or not to cover the tuition cost after four years. If tuition cost is $26,537 for one year. If f(t)=450t for 18 years at 7% annual interest rate by using the equation from exercise 79 and 80.

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