Uncle Fred recently died and left $340,000 to his 55-year-old favorite niece. She immediately spent $90,000...

Uncle Fred recently died and left $340,000 to his 55-year-old favorite niece. She immediately spent $90,000 on a town home but decided to invest the balance for her retirement at age 65. What rate of return must she earn on her investment over the next 10 years to permit her to withdraw $65,000 at the end of each year through age 85 if her funds earn 12 percent annually during retirement? Use Appendix A and Appendix D to answer the question. Round your answer to the nearest whole number.

Solutions

Expert Solution

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$ 65,000.00
Int Rate	12.0000%
Periods	20

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 65000 * [ 1 - [(1+0.12)^-20]] /0.12
= $ 65000 * [ 1 - [(1.12)^-20]] /0.12
= $ 65000 * [ 1 - [0.1037]] /0.12
= $ 65000 * [0.8963]] /0.12
= $ 485513.84
Amount deposited at 55 Years:

Amount inherited = $ 340000

Amount spent on Home = $ 90000

Amount deposited for retirement = $ 250000 ( $ 340000 - $ 90000 )

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$ 250,000.00
Future Value	$ 485,513.84
Periods	10

Future Value = Cash Flow * ( 1 + r )^n
$ 485513.84 = $ 250000 ( 1 + r ) ^ 10
( 1 + r ) ^ 10 = $485513.84 / $250000
( 1 + r ) ^ 10 = 1.9421
( 1 + r ) = 1.9421 ^ ( 1 / 10 )
( 1 + r ) = 1.0686
r = 1.068627 - 1
r = 0.068627 i.e 6.86 %

Pls comment, if any further assistance is required.

jeff jeffy answered 1 year ago

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