Question

Your client is 21 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $7,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 11% in the future. If she follows your advice, how much money will she have at 65? Do not round intermediate calculations. Round your answer to the nearest cent. $   How much will she have at 70? Do not round intermediate calculations. Round your answer to the nearest cent. $   She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Do not round intermediate calculations. Round your answers to the nearest cent. Annual withdrawals if she retires at 65: $ Annual withdrawals if she retires at 70: $

Answer 1

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Part A:

Particulars	Amount
Cash Flow	$      7,000.00
Int Rate	11.000%
Periods	44

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 7000 * [ [ ( 1 + 0.11 ) ^ 44 ] - 1 ] / 0.11
= $ 7000 * [ [ ( 1.11 ) ^ 44 ] - 1 ] / 0.11
= $ 7000 * [ [98.6759] - 1 ] / 0.11
= $ 7000 * [97.6759] /0.11
= $ 6215738.66

Part B:

Particulars	Amount
Cash Flow	$      7,000.00
Int Rate	11.000%
Periods	49

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 7000 * [ [ ( 1 + 0.11 ) ^ 49 ] - 1 ] / 0.11
= $ 7000 * [ [ ( 1.11 ) ^ 49 ] - 1 ] / 0.11
= $ 7000 * [ [166.2746] - 1 ] / 0.11
= $ 7000 * [165.2746] /0.11
= $ 10517475.73

Part C:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

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

If She Retires at 65:

Particulars	Amount
PV Annuity	$ 62,15,738.66
Int Rate	11.000%
Periods	20

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 6215738.66 / [ 1 - [(1+0.11)^-51]] /0.11
= $ 6215738.66 / [ 1 - [(1.11)^-51]] /0.11
= $ 6215738.66 / [ 1 - 0.124 ] /0.11
= $ 6215738.66 / [0.876 / 0.11 ]
= $ 6215738.66 / 7.9633
= $ 780545.34
Amount can be with drawn each Year is $ 780545.34

If she retires at 70 :

Particulars	Amount
PV Annuity	$ 1,05,17,475.73
Int Rate	11.000%
Periods	15

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 10517475.73 / [ 1 - [(1+0.11)^-51]] /0.11
= $ 10517475.73 / [ 1 - [(1.11)^-51]] /0.11
= $ 10517475.73 / [ 1 - 0.209 ] /0.11
= $ 10517475.73 / [0.791 / 0.11 ]
= $ 10517475.73 / 7.1909
= $ 1462615.28

AMount can be withdrawn each year is $ 1462615.28

Pls comment, if any further assistance is required.