Question

eBook Problem 7-28 You contribute $1,000 annually to a retirement account for ten years and stop making payments at the age of 45. Your twin brother (or sister . . . whichever applies) opens an account at age 45 and contributes $1,000 a year until retirement at age 65 (20 years). You both earn 9 percent on your investments. How much can each of you withdraw for 20 years (that is, ages 66 through 85) from the retirement accounts? Use Appendix A, Appendix C, and Appendix D to answer the question. Round your answers to the nearest dollar. You can withdraw $   . Your twin can withdraw $

Answer 1

Computation of Balance in the Account at the age of 45

We know that Future Value of Ordinary Annuity = C [{ ( 1+i)^n -1}/i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

Future value = $ 1000[ { ( 1+0.09) ^ 10 - 1 } /0.09]

= $ 1000[ { ( 1.09)^10 - 1} /0.09]

= $1000 [ { 2.367364-1} /0.09]

= $ 1000[ 1.367364/0.09]

= $1000*15.19293

= $ 15192.93

Hence Balance available at the age of 45 is $ 15192.93

Computation of Balance Available in the Account at the aage of 65

We know that Future value = Present value( 1+i)^n

Here I = Rate of interest n = No.of Years

Future value = $ 15192.93( 1.09)^20

= $ 15192.93* 5.604411

= $ 85147.42

Hence Balance available in the account at the age of 65 is $ 85147.42

Computation of Amount can be withdrawn

We know that present value of the future payments should be equal to $ 85147.42

We know that Present value of Annuity = C [ {1- ( 1+i)^-n }/i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

$ 85147.42= C [ { 1-( 1.09)^-20 } /0.09]

$ 85147.42 = C [ { 1-0.178431} /0.09]

$ 85147.42 = C [ 0.821569/0.09]

$ 85147.42 = C [ 9.128546]

$ 85147.42/9.128546 = C

C = $ 9328

Amount Can be withdrawn every year is$ 9328

Computation of Balance in the account of twin brother at the age of 65.

We know that Future Value of Ordinary Annuity = C [{ ( 1+i)^n -1}/i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

Future value = $ 1000[ { ( 1+0.09) ^ 20- 1 } /0.09]

= $ 1000[ { ( 1.09)^20 - 1} /0.09]

= $1000 [ { 5.604411-1} /0.09]

= $ 1000[ 4.604411/0.09]

=$1000*51.16012

= $ 51160.12

Computation of Amount can be withdrawn by Twin Brother.

We know that present value of the future payments should be equal to $ 51160.12

We know that Present value of Annuity = C [ {1- ( 1+i)^-n }/i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

$ 51160.12= C [ { 1-( 1.09)^-20 } /0.09]

$ 51160.12= C [ { 1-0.178431} /0.09]

$ 51160.12= C [ 0.821569/0.09]

$ 51160.12 = C [ 9.128546]

$ 51160.12/9.128546 = C

C = $ 5604

Amount Can be withdrawn every year is$ 5604.

You can withdraw $ 9328

Your twin brother can withdraw $ 5604

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