Question

Retirement Problem budget plan. Please fill out whole thing.

RETIREMENT PROBLEM How much do you want to spend monthly when you reti you must determine how big of a "nest egg you need want to spend monthly when you retire? To determine if your goal is feasible and for adequate, influenced by your age at retirement une how big of a "nest ego" you need when you retine. The optimal size of the nest egg is your age at retirement, life expectancy savings and the interest you earn. Historically, the stock market provides an average our between a provides an average return between 89-12However, if you do not want your life savings to be 100 invested in the stock market; you may use a lower interest rate, say 5%. Answer the following: A. How much money do you want to spend monthly after retiring? PMT = B. At what age do you expect to pass away" (You can go to deathclock.com to estimate your life expectancy or utilized the attached actuary table.) - C. At what age do you expect to retire? D. Subtract from B. E. Multiply D by 12. N= - F. What annual rate of interest do you expect to eam on your nest egg? I = 12 G. Let FV = 0. Solve for PV. PV = Now, we need to determine how much you must save monthly to achieve your goal. H. Let FV = the PV you calculated in G above. FV = I. At what age will you retire (see C above)? J. At what age will start saving for your retirement? K. Subtract from I and multiple by 12. N= * 12 = L. What annual rate of interest do you expect to earn on your savings? (Realistically, it may be more than the rate you used in F above. As people get older, they reduce their exposure to risk, i.e., willing to accept a lower return on their savings.) Use whatever interest rate you think is reasonable. TE /12= M. Let PV =0. (If you already have savings, you may rework this later with PV equaling your current savings.) N. Solve for PMT. PMT = Do you think your goal is obtainable? (Circle your decision.) Yes No Do you think your goal is adequate? (Circle your decision.) Yes No P. Now, let: N= E + K = PMT=0 FV AE I= .25 (I represents an inflation rate of 3%/12. Solve for PV = PV indicates approximately how much your last withdrawal from your nest egg is worth in today's dollars. In PV seems inadequate you may need to go back and change your plans. Note these calculations do not factor in the taxes you would have to pay or other sources of income such as social security and pensions. Do you still think your goal is adequate? (Circle your decision.) Yes No Defend your answer!

The funds can be made up by yourself it doesnt really matter how its done.

Answer 1

(A)

$1000

(B)

80 year

(C)

65 year

(D)

80 - 65 = 15 years

(E)

N = 15x12 = 180 months

(F)

i = 0.06/12 =0.005

(G)

PV = 1000(1 + v + v² + v³ + ............+ v¹⁷⁹)

where v = (1+i)^-1 = 1.005^-1

$\large \Rightarrow$ PV = 1000{(1 - v¹⁸⁰) / v} = 1000{(1 - 1.005^-180) / (1 - 1.05^-1) = $119096

(H)

FV = $119096

(I)

65 year

(J)

50 year

(K)

N =12x(65 - 50) = 180 months

(L)

j = 0.09/12= 1.0075

(M)

PV = 0

(N)

119096 = PMT.{ (1+j)¹⁸⁰ + (1+j)¹⁷⁹ + (1+j)¹⁷⁸ + ..........+ (1+j) }

$\large \Rightarrow$ 119096 = PMT.(1+j)[{(1+j)¹⁸⁰ - 1} / (1+j-1)]

$\large \Rightarrow$119096 = PMTx1.0075x{(1.0075¹⁸⁰ - 1) / 0.0075}

$\large \Rightarrow$ 119096 = PMTx381.2438

$\large \Rightarrow$ PMT = $312.38

The goal is obtainable and adequate

(P)

PV = 1000x1.0025^-180 = $639

The goal is adequate.