(a) Explanation Given Information: The amount of $ 500 is deposited in an account at the interest rate of 4 % and the interest is compounded annually. Formula used: The formula to compute the balance amount after t years when interest is compounded n times per year is, A = P ( 1 + r n ) n t Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals, t is the number of years and n is the number of times compounded per year. The property of logarithms for the expression ln x n is ln x n = n ln x where x and y are real numbers greater than 0 . Calculation: Consider that the amount of $ 500 is deposited in an account at the interest rate of 4 % and the interest is compounded annually. Here, P = $ 500 , r = 4 % . The number of times compounded per year is 1 as the interest is compounded annually, that is, n = 1 . As the amount will become double of the deposited amount after t years, then the amount after t years is 2 P , that is, A = 2 P = 2 ( $ 500 ) = $ 1000 Simplify the rate as, r = 4 % = 4 100 = 0.04 Substitute 0.04 for interest rate, $ 500 for the amount deposited, 1 for a number of times compounded per year and $ 1000 for the amount after t years in the formula, A = P ( 1 + r n ) n t as, $ 1000 = $ 500 ( 1 + 0 (b) To determine To calculate: The time required so that the deposited amount will become double if the amount of $ 500 is deposited in an account at the interest rate of 4 % and the interest is compounded monthly. (c) To determine To calculate: The time required so that the deposited amount will become double if the amount of $ 500 is deposited in an account at the interest rate of 4 % and the interest is compounded daily. (d) To determine To calculate: The time required so that the deposited amount will become double if the amount of $ 500 is deposited in an account at the interest rate of 4 % and the interest is compounded continuously.

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 4, Problem 20TYS

(a)

To determine

To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded annually.

(b)

To determine

To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded monthly.

(c)

To determine

To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded daily.

(d)

To determine

To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded continuously.

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Chapter 4, Problem 19TYS

Chapter 4, Problem 21TYS

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Chapter 4 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the formula for the ratio of carbon isotopes...Ch. 4.1 - Prob. 4CP Ch. 4.1 - Prob. 5CP Ch. 4.1 - Prob. 1SWU Ch. 4.1 - Prob. 2SWU Ch. 4.1 - Prob. 3SWU Ch. 4.1 - Prob. 4SWU Ch. 4.1 - Prob. 5SWU

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The time required so that the deposited amount will become double if the amount of $ 500 is deposited in an account at the interest rate of 4 % and the interest is compounded annually.

Solution Summary: The author calculates the time required to double the amount of 500 when the interest is compounded annually.

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To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded annually.

To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded monthly.

To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded daily.

To calculate: The time required so that the deposited amount will become double if the amount of $500 is deposited in an account at the interest rate of 4% and the interest is compounded continuously.

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Chapter 4 Solutions