Explanation Given information: Person X is planning to maintain a balance for retirement for the upcoming 30 years. Thus, Person X will invest $850 and $350 in stock and bond account respectively. The return from the stock and bond account is 10% and 6% respectively. However, Person X will combine the amount of two accounts into one account with 5% return, when he retires. The period of withdrawal is assumed for 25 years. Note : We must remember that the rate of interest is different for the two accounts in the timeline. We must compute the annuity payment at the time of retirement. The savings for retirement ends and the withdrawals of retirement begins. Hence, the present value of the retirement withdrawal will be the future value of the savings of retirement. Thus, we must compute the future value of the stock and bond account and then we must take the sum of the two future values. Equation to calculate the future value annuity: Future value annuity = C { [ ( 1 + r ) t − 1 ] r } Note: C denotes the annual cash flow or annuity payment, r denotes the rate of interest, and t denotes the period. Compute the future value annuity for stock account: Future value annuity = C { [ ( 1 + r ) t − 1 ] r } = $ 850 [ ( 1 + 0.10 12 ) 30 × 12 − 1 0.10 12 ] = $ 850 [ ( 1 + 0.008333333333 ) 360 − 1 0.008333333333 ] = $ 850 [ ( 1.008333333 ) 360 − 1 0.008333333333 ] = $ 850 [ 19.83739935 − 1 0.008333333333 ] = $ 850 [ 18.83739935 0.008333333333 ] = $ 850 × 2 , 260.487922 = $ 1 , 921414.73 Note: The investment amount and the rate of return for stock account are $850 and 10% respectively. To compute the monthly return, divide the rate by 12 and multiply the number of periods by 12. Hence, the future value annuity for stock account is $1, 921414.73 . Compute the future value annuity for bond account: Future value annuity = C { [ ( 1 + r ) t − 1 ] r } = $ 350 [ ( 1 + 0.06 12 ) 30 × 12 − 1 0.10 12 ] = $ 350 [ ( 1 + 0.005 ) 360 − 1 0.005 ] = $ 350 [ ( 1.005 ) 360 − 1 0.005 ] = $ 350 [ 6.022575212 − 1 0.005 ] = $ 350 [ 5

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Author: Ross

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Retirement Income

Retirement income is the income received by the retiring person after retirement. Income can either be paid every month or paid annually. The retiree would get a guaranteed income until their death. Retirement income payment differs from person to person…

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Chapter 6, Problem 32QP

Summary Introduction

To calculate: The amount that Person X can withdraw every month

Introduction:

An annuity is a level stream of flow of cash for a particular period. They often appear in financial arrangements and it is used as a shortcut to find the values.

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Chapter 6, Problem 31QP

Chapter 6, Problem 33QP

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The amount that Person X can withdraw every month Introduction: An annuity is a level stream of flow of cash for a particular period. They often appear in financial arrangements and it is used as a shortcut to find the values.

Solution Summary: The author explains that an annuity is a level stream of cash flow for the upcoming 30 years.

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To calculate: The amount that Person X can withdraw every month Introduction: An annuity is a level stream of flow of cash for a particular period. They often appear in financial arrangements and it is used as a shortcut to find the values.

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Chapter 6 Solutions

To calculate: The amount that Person X can withdraw every month

Introduction:

An annuity is a level stream of flow of cash for a particular period. They often appear in financial arrangements and it is used as a shortcut to find the values.