# Ann E. Belle is age 45 and pla

Ann E. Belle is age 45 and plans to retire in 20 years (at age65). She has retirement savings in a mutual fund account, which hasa current balance of \$150,000 (Ann does not plan to add anyadditional money to this account). Also, Ann opened a 401Kretirement account with her new employer and will contribute\$15,000 per year into her 401K until retirement.

solve question algebraically and show work.

1.)If Ann’s 401K account grows at an annual rate of 8.0% peryear, how much money will Ann have in her 401K account at age65?

2.) at retirement, Ann plans take the investment balance fromher mutual fund account and the balance from her 401K account andcombine them into an IRA account. To minimize risk, her IRA accountwill invest in more conservative securities. As a result, Annanticipates her annual IRA returns to be about 5.0% duringretirement.   While in retirement, Susan plans towithdraw \$100,000 per year from her IRA account over the next 25years. Is this possible? Explain why or why not?

 PV of annuity for making pthlypayment P = PMT x (((1-(1 + r) ^- n)) /r) Where: P = the present value of an annuitystream A PMT = the dollar amount of eachannuity payment \$        100,000 r = the effective interest rate (alsoknown as the discount rate) 5% n = the number of periods in whichpayments will be made 25 PV of retirement corpusneeded= PMT x (((1-(1 + r) ^- n)) /r) PV of retirement corpusneeded= 100000* (((1-(1 + 5%) ^-25)) /5%) PV of retirement corpusneeded= \$ 1,409,394.46 So the retirement corpus required is \$1,409,394.46. Fundingsource MutualFund Current balance \$        150,000 Interest 8% Time 20 Amount at the time ofretirement 150000*(1+8%)^20 Amount at the time ofretirement \$   699,143.57 Remaining corpus required= 1409394.46-699143.57 Remaining corpus required= \$   710,250.89 Fundingsource 401(K)Fund FV of annuity P = PMT x ((((1 + r) ^ n) – 1) /r) Where: P = the future value of an annuitystream A PMT = the dollar amount of eachannuity payment \$          15,000 r = the effective interest rate (alsoknown as the discount rate) 8% n = the number of periods in whichpayments will be made 20 FV of annuity= PMT x ((((1 + r) ^ n) – 1) /r) FV of annuity= 15000* ((((1 + 8%) ^20) – 1) /8%) FV of annuity= \$   686,429.46 As we can see that the FV of annuitydoes not provide the requisite FV, it is not possible to set upthis arrangement.

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