You are now 50 years old and plan to retire at age 65. You currently have a stoc

Question

You are now 50 years old and plan to retire at age 65. You currently have a stock portfolio worth $150,000, a 401(k) retirement plan worth $250,000 and a money market account worth $50,000. Your stock portfolio is expected to provide you annual returns of 12 percent, your 401(k) investment will earn you 9.5 percent annually, and the money market account earns 5.25 percent, compounded monthly. a. If you do not save another penny for the next 15 years, how much will you have from your current savings when you retire at age 65? Hint: Determine the future value of each account and then the grand total of all three.                                                                                    Use the future value of a lump sum equation as well as the FV function: FV(rate,nper,pmt,pv,type) Current age: Retirement age: Stock Portfolio Current value of stock portfolio: Expected return on portfolio: Years to retirement: Expected value of portfolio at age 65 (formula): Expected value of portfolio at age 65 (function): 401k Plan Current value of 401k portfolio: Expected return on portfolio: Years to retirement: Expected value of portfolio at age 65 (formula): Expected value of portfolio at age 65 (function): Money Market Account Current value of stock portfolio: Expected return on portfolio: Years to retirement: Frequency of compounding: Expected value of portfolio at age 65 (formula): Expected value of portfolio at age 65 (function): Total of all three investments: b. Assume you plan to invest $12,000 every year in your 401K plan for the next 15 years starting next year. How much will you have in total at retirement? Annual investment in 401k plan: Expected return on portfolio: Value of 401k plan investments (formula): Value of 401k plan investments (function): Total investment amount at retirement: c. Assume that you expect to live another 25 years after retirement (i.e., until age 90). You now take all of your investments (use scenario from part b), and invest it in an account paying 8 percent. If you plan to use all your savings starting a year from retirement, how much can you withdraw every year for the next 25 years and leave nothing in your account at age 90? Hint: Solve for the PMT using the present value of an annuity equation and then use the PMT function: PMT(rate,nper,pv,fv,type). Amount available at retirement: Length of planned withdrawals (years): Expected return on investments: Amount of each yearly withdrawal (formula): Amount of each yearly withdrawal (function): d. If you wanted a perpetuity, how much will you be able to withdraw each year starting a year from now without touching your principal? Type of payment: Present value of perpetuity: Expected return on investment: Amount of each yearly withdrawal: You are now 50 years old and plan to retire at age 65. You currently have a stock portfolio worth $150,000, a 401(k) retirement plan worth $250,000 and a money market account worth $50,000. Your stock portfolio is expected to provide you annual returns of 12 percent, your 401(k) investment will earn you 9.5 percent annually, and the money market account earns 5.25 percent, compounded monthly. a. If you do not save another penny for the next 15 years, how much will you have from your current savings when you retire at age 65? Hint: Determine the future value of each account and then the grand total of all three.                                                                                    Use the future value of a lump sum equation as well as the FV function: FV(rate,nper,pmt,pv,type) Current age: Retirement age: Stock Portfolio Current value of stock portfolio: Expected return on portfolio: Years to retirement: Expected value of portfolio at age 65 (formula): Expected value of portfolio at age 65 (function): 401k Plan Current value of 401k portfolio: Expected return on portfolio: Years to retirement: Expected value of portfolio at age 65 (formula): Expected value of portfolio at age 65 (function): Money Market Account Current value of stock portfolio: Expected return on portfolio: Years to retirement: Frequency of compounding: Expected value of portfolio at age 65 (formula): Expected value of portfolio at age 65 (function): Total of all three investments: b. Assume you plan to invest $12,000 every year in your 401K plan for the next 15 years starting next year. How much will you have in total at retirement? Annual investment in 401k plan: Expected return on portfolio: Value of 401k plan investments (formula): Value of 401k plan investments (function): Total investment amount at retirement: c. Assume that you expect to live another 25 years after retirement (i.e., until age 90). You now take all of your investments (use scenario from part b), and invest it in an account paying 8 percent. If you plan to use all your savings starting a year from retirement, how much can you withdraw every year for the next 25 years and leave nothing in your account at age 90? Hint: Solve for the PMT using the present value of an annuity equation and then use the PMT function: PMT(rate,nper,pv,fv,type). Amount available at retirement: Length of planned withdrawals (years): Expected return on investments: Amount of each yearly withdrawal (formula): Amount of each yearly withdrawal (function): d. If you wanted a perpetuity, how much will you be able to withdraw each year starting a year from now without touching your principal? Type of payment: Present value of perpetuity: Expected return on investment: Amount of each yearly withdrawal:

Explanation / Answer

Answer:a. Stock Portfolio

Current value of stock portfolio = $150,000

Expected return on portfolio = i = 12%

Time to retirement = n = 15 years

Expected value of portfolio at age 65 = FV Stock

FV Stock = PV (1 +i)15= $150,000* (1.12)15= $821,034.86

410(k) Investment

Current value of 410(k) portfolio = $250,000

Expected return on portfolio = i= 9.5%

Time to retirement = n = 15 years

Expected value of portfolio at age 65 = FV401k

FV401k = PV (1+i )15= $250,000 (1.095)15= $975,330.48

Money market account

Current value of savings = $50,000

Expected return on portfolio = i = 5.25%

Time to retirement = n = 15 years

Frequency of compounding = m = 12

Expected value of portfolio at age 65 = FVMMA

FVMMA=PV*(1+i/m)m*n

=$50000*(1+0.0525/12)12*15

=50000*2.1941=$109706.14

Total value of all three investments = $821,034.86 + $975,330.48 + $109,706.14=

$1,906,071.48

Answer:b Planned annual investment in 401k plan = $12,000

Future value of annuity = FVA

FVAn=PMT(((1+i)n-1)/i))

=$12000*(1.095)15-1/0.095)

=$12000*30.5402

=$366482.77

Answer:c

Amount available at retirement = PVA = $2,272,554.25

Length of annuity = n = 25

Expected return on investment = i = 8%

Annuity amount expected = PMT

Using the PVA equation:

PVAn=PMT*[[1-(1/(1+i)n]/i]

PMT=$2,272,554.25/[[1-(1/(1.08)25]/0.08]

=$2,272,554.25/10.6748

=$212889.63

Each payment received for the next 25 years will be $212,889.63

Answer:d Type of payment = Perpetuity

Present value of perpetuity = PVA = $2,272,554.25

Expected return on investment = i = 8%

PV of perpetuity=PMT/i

$2,272,554.25=PMT/0.08

$181,804.34

You could receive an annual payment of $181,804.34 forever.

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