Explanation Given Information: The winner of May 18, 2013, Powerball, sets aside $150 million after-tax amount in a fund earning at interest rate of 4.5 % which is compounded monthly, after a deferred payment of 16 years for the next 50 years. Formula used: The present value of a deferred annuity of $ R per period for n number of periods, deferred for k number of periods with rate of interest i per period is, A ( n , k ) = R [ 1 − ( 1 + i ) − n i ] ( 1 + i ) − k Calculation: Consider the provided information: The winner of May 18, 2013, Powerball, sets aside $150 million after-tax amount in a fund earning at interest rate of 4.5 % which is compounded monthly, after a deferred payment of 16 years for the next 50 years. According to the information, The winner of May 18, 2013, Powerball, sets aside $150 million. Hence, A ( n , k ) = 150 , 000 , 000 And the amount is to be withdrawn in 50 monthly payments. n = 50 × 12 = 600 Since, it is after a deferred payment of 16 years, k = 12 × 16 = 192 The interest rate is 4.5 % compounded monthly. i = 4.5 100 × 1 12 = 0.00375 The present value of the deferred due will be: A ( n , k ) = R [ 1 − ( 1 + i ) − n i ] ( 1 + i ) − k Substitute 150 , 000 , 000 for A ( n , k ) , 0

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 6.4, Problem 55E

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To calculate: The amount that is available to the winner’s heirs for the next 50 years at the end of each month.

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Chapter 6.4, Problem 54E

Chapter 6.4, Problem 56E

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Chapter 6 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 6.1 - CHECKPOINT 1. What is the simple interest...Ch. 6.1 - CHECKPOINT 2. If $8000 is invested at 6% simple...Ch. 6.1 - CHECKPOINT 3. If a $2500 investment grows to $2875...Ch. 6.1 - Prob. 4CP Ch. 6.1 - CHECKPOINT 5. Given the arithmetic sequence...Ch. 6.1 - Prob. 1E Ch. 6.1 - SIMPLE INTEREST In Problems 1-4, find the...Ch. 6.1 - SIMPLE INTEREST In Problems 1-4, find the...Ch. 6.1 - Prob. 4E Ch. 6.1 - 3. $10,000 is invested for 6 years at an annual...

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The amount that is available to the winner’s heirs for the next 50 years at the end of each month.

Solution Summary: The author calculates the amount that is available to the winner's heirs for the next 50 years at the end of each month.

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To calculate: The amount that is available to the winner’s heirs for the next 50 years at the end of each month.

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Chapter 6 Solutions