Question

Problem 7-03 A 50-year-old woman decides to put funds into a retirement plan. She can save $1,000 a year and earn 5 percent on this savings. How much will she have accumulated if she retires at age 65? Use Appendix C to answer the question. Round your answer to the nearest dollar. $ _____ At retirement how much can she withdraw each year for 20 years from the accumulated savings if the savings continue to earn 5 percent? Use Appendix D to answer the question. Round your answer to the nearest dollar. $ _____

Answer 1

Part A:

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

Particulars	Amount
Cash Flow	$      1,000.00
Int Rate	5.000%
Periods	15

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 1000 * [ [ ( 1 + 0.05 ) ^ 15 ] - 1 ] / 0.05
= $ 1000 * [ [ ( 1.05 ) ^ 15 ] - 1 ] / 0.05
= $ 1000 * [ [2.0789] - 1 ] / 0.05
= $ 1000 * [1.0789] /0.05
= $ 21578.56

Amount in Account at the time of Retirement is $ 21578.56

Part B:

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

Particulars	Amount
PV Annuity	$          21,578.56
Int Rate	5.000%
Periods	20

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 21578.56 / [ 1 - [(1+0.05)^-240]] /0.05
= $ 21578.56 / [ 1 - [(1.05)^-240]] /0.05
= $ 21578.56 / [ 1 - 0.3769 ] /0.05
= $ 21578.56 / [0.6231 / 0.05 ]
= $ 21578.56 / 12.4622
= $ 1731.52

She can withdraw $ 1731.52 each year for Next 20 Years.