Explanation Given Information: An amount of $ 2000 is invested in an account for 10 years at the rate of interest which is compounded as: (a). r = 5 % , compounded continuously (b). r = 6 % , compounded quarterly Calculation: Consider that the amount of $ 2000 is invested in an account for 10 years. Here, P = $ 2000 and t = 10 . Now, consider the part (a) with the interest rate of 5 % that is compounded continuously, Simplify the rate as, r = 5 % = 5 100 = 0.05 The formula to compute the balance amount after t years when interest is compounded continuously is, A = P e r t Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals and t is the number of years. Compute the balance amount by substituting 0.05 for interest rate, $ 2000 for the amount deposited and 10 years for the time in the formula “ A = P e r t ” as, A = $ 2000 e ( 0.05 ) ( 10 ) = $ 2000 e 0.5 ≈ $ 2000 × 1.64872 = $ 3297.44 Thus, the balance amount in the account when interest is compounded continuously at the rate of 5 % is approximately $ 3297.44 . Now, consider the part (b) with the interest rate of 6 % that is compounded quarterly, Simplify the rate as, r = 6 % = 6 100 = 0

CALCULUS APPLIED APPROACH >PRINT UGRADE<

10th Edition

ISBN: 9780357667231

Author: Larson

Publisher: CENGAGE L

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Chapter 4, Problem 23RE

To determine

The account which has more balance after 10 years from the following options when an amount of $2000 is invested in an account at the rate of interest which is compounded as:

(a). r=5%, compounded continuously

(b). r=6%, compounded quarterly

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Chapter 4 Solutions

CALCULUS APPLIED APPROACH >PRINT UGRADE<

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 account which has more balance after 10 years from the following options when an amount of $ 2000 is invested in an account at the rate of interest which is compounded as: (a). r = 5 % , compounded continuously (b). r = 6 % , compounded quarterly

Solution Summary: The author explains how an amount of 2000 is invested in an account for 10 years at the rate of interest which is compounded.

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The account which has more balance after 10 years from the following options when an amount of $2000 is invested in an account at the rate of interest which is compounded as:

(a). r=5%, compounded continuously

(b). r=6%, compounded quarterly

Chapter 4 Solutions

The account which has more balance after 10 years from the following options when an amount of $ 2000 is invested in an account at the rate of interest which is compounded as: (a). r = 5 % , compounded continuously (b). r = 6 % , compounded quarterly

Solution Summary: The author explains how an amount of 2000 is invested in an account for 10 years at the rate of interest which is compounded.

Concept explainers

Videos

The account which has more balance after 10 years from the following options when an amount of $2000 is invested in an account at the rate of interest which is compounded as: (a). r=5%, compounded continuously (b). r=6%, compounded quarterly

Chapter 4 Solutions

The account which has more balance after 10 years from the following options when an amount of $2000 is invested in an account at the rate of interest which is compounded as:

(a). r=5%, compounded continuously

(b). r=6%, compounded quarterly