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Saving for College When your first child is born, you begin to save for college by depositing $400 per month in an account paying 12% interest per year. With a continuous stream of investment and continuous compounding, how much will you have accumulated in the account by the time your child enters college 18 years later?

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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203

Solutions

Chapter
Section
BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203
Chapter 14.4, Problem 48E
Textbook Problem
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Saving for College When your first child is born, you begin to save for college by depositing $400 per month in an account paying 12% interest per year. With a continuous stream of investment and continuous compounding, how much will you have accumulated in the account by the time your child enters college 18 years later?

To determine

To calculate: The Future value of the investment accumulated in the account by the time child enters college 18 years later where, $400 per month is been invested in an account with interest rate of 12% per year.

Explanation of Solution

Given Information:

The amount of $400 per month is been invested in an account with interest rate of 12% per year.

Formula used:

The Future Value of a Continuous Income Stream:

If the rate of receipt of Income from time t=a to t=b is R(t) dollars per unit of time and the rate of interest is r per unit time on the deposited Income, compounded continuously, then at time t=b amount of money would be:

FV=abR(t)er(bt)dt

Calculation:

Total saving per year is:

$400×12=4,800 per year.

Consider the investment equation:

R(t)=4,800

Since, to get Future value of the investment accumulated in 18 years the interval is:

0t18

Breaking the given interval 0t18 to get:

[0,18]

Where,

a=0b=18

Rate of interest is given by 12%, simplifying it to get:

r=12100r=0

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Chapter 14 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)
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In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - Sales Your monthly sales of green tea ice cream...Ch. 14.6 - Profit Your monthly profit on sales of avocado ice...Ch. 14.6 - Newtons Law of Cooling For coffee in a ceramic...Ch. 14.6 - Newtons Law of Cooling For coffee in a paper cup,...Ch. 14.6 - Cooling A bowl of clam chowder at 190F is placed...Ch. 14.6 - Heating Suppose that a pie at 20F is put in an...Ch. 14.6 - Market Saturation You have just introduced a new...Ch. 14.6 - Market Saturation Repeat Exercise 27, assuming...Ch. 14.6 - Determining Demand Nancys Chocolates estimates...Ch. 14.6 - Determining Demand Nancys Chocolates estimates...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Approach to Equilibrium The Extrasoft Toy Co. has...Ch. 14.6 - Approach to Equilibrium Spacely Sprockets has just...Ch. 14.6 - Logistic Equation There are many examples of...Ch. 14.6 - Logistic Equation Using separation of variables...Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - What is the difference between a particular...Ch. 14.6 - Why is there always an arbitrary constant in the...Ch. 14.6 - Show by example that a second-order differential...Ch. 14.6 - Find a differential equation that is not...Ch. 14.6 - Find a differential equation whose general...Ch. 14.6 - Explain how, knowing the elasticity of demand as a...Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 23 and 24, calculate the consumers...Ch. 14 - In Exercises 23 and 24, calculate the consumers...Ch. 14 - In Exercises 25 and 26, calculate the consumers...Ch. 14 - In Exercises 25 and 26, calculate the consumers...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - Spending on Stationery Alarmed by the volume of...Ch. 14 - Spending on Shipping During the past 10 months,...Ch. 14 - Education Costs Billy-Sean OHagan, having...Ch. 14 - Investments OHaganBooks.com keeps its cash...Ch. 14 - Consumerss and Producerss Surplus Currently, the...Ch. 14 - Consumers and Producers Surplus OHaganBooks.com is...Ch. 14 - Revenue Sales of the best seller A River Burns...Ch. 14 - Foreign Investments Panicked by the performance of...Ch. 14 - Investments OHaganBooks.com CEO John OHagan has...Ch. 14 - Savings John OHagan had been saving money for...Ch. 14 - Acquisitions The Megabucks Corporation is...Ch. 14 - More Acquisitions OHaganBooks.com is thinking of...Ch. 14 - Incompetence OHaganBooks.com is shopping around...Ch. 14 - Shrewd Bankers The new junior officer at the bank...

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