Question

2. Mrs. D who 27 years old plans to retire at the age of 55. Mrs. D would like to be able to withdraw $132,000 per year from her retirement account for 454 years after retirement beginning the year after her retirement. She is also expecting an inheritance of $54,000 to be transferred to her on her 35th birthday. a How much does she need to have in her retirement account by retirement- date if the interest rate is 6% per year during the post-retirement years?- b Suppose she already has $12,000 in her retirement investment account that earns 9% per year. What will be the value of this amount by her retirement date? c Given her goal, her expected inheritance, and the investment she already has in lb, how much does she need to invest per year from now till retirement (at 9% annual rate of return) in order to reach her retirement goal?

Answer 1

2)

a)

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, P = Annuity = 132000, i = Interest Rate = 0.06, n = Number of Periods = 45

PV = 132000*[1-{(1+0.06)^-45}]/0.06 = 132000*0.92735/0.06 = $2040169.84

b)

Future Value = Present Value*[(1+Interest Rate)^Number of Years]

= 12000*[(1+0.09)^(55-27)] = 12000*11.1671385 = $134005.67

c)

Future Value of Inheritance = Present Value*[(1+Interest Rate)^Number of Years] = 54000*[(1+0.09)^(55-35)] = 54000*5.60441 = $302638.18

Balance Amount that needs to be accumulated by monthly payments = Total Amount required at 55-FV of current balance of 12000+FV of Inheritance = 2040169.84-134005.67-302638.18 = $1603525.99

FV of Annuity = P*[{(1+i)^n}-1]/i

Where, FV = 1603525.99, i = Interest Rate = 0.09, n = Number of Periods = 55-27 = 28

Therefore,

1603525.99 = P*[{(1+0.09)^28}-1]/0.09

144317.3391 = P*10.1671395

Therefore, Amount to be deposited every Year till retirement = P = 144317.3391/10.1671395 = $14194.49

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