Your client is planning for retirement. Calculate the size of the monthly contri
ID: 2718953 • Letter: Y
Question
Your client is planning for retirement. Calculate the size of the monthly contributions he will need to make to achieve his retirement goals. He is hoping to retire in exactly 32 years from today. He will make equal monthly contributions to his retirement account during these 32 years, with the first deposit in exactly one month from today. Currently, he has savings of $12,000, which he is going to transfer immediately into this new retirement account. He will also receive an insurance pay equal to $550,000 as soon as he retires. During his retirement years, he is expecting to make 12 annual withdrawals in the size of $150,000 per year, with the first withdrawal to take place as soon as he retires. At the end of the sixth year of his retirement he will need to withdraw an additional amount of $45,000 in order to cover the expenses of a transcontinental cruise. After the 12 years in retirement, he is planning on moving into a retirement village. This facility will provide housing and all other necessities for the rest of his life. In exchange, he will need to make a one-time payment of $1.5 million at the time of move-in, i.e., after 12 years in retirement. During the next 32 years, funds in the retirement account will be invested into a mix of securities that are expected to generate an average annual return of 8%. After he retires, the investments will be shifted to safer securities with an average expected annual return of 5% p.a.
Explanation / Answer
Amount need at the time of retirement = PV of annual withdrawl + PV of additional amount of withdrawl in six year + Pv of one time payment in 12 year
Amount need at the time of retirement = Annual Amount*(1-(1+r)^-n)/r*(1+r) + Additional Amount*(1+r)^-6 + One Time Payment*(1+r)^-12
Amount need at the time of retirement = 150000*(1-(1+5%)^-12)/5% * (1+5%) + 45000*(1+5%)^-6 + 1500000*(1+5%)^-12
Amount need at the time of retirement = $ 2,264,797.95
Amount Available from insurance = 550000
Net Amount required = 2264797.95 -550000 = $ 1,714,797.95
Monthly Contribution = pmt(rate,nper,pv,fv)
rate = 8%/12
nper = 32*12 = 384
pv = -12000
fv = 1714797.95
Monthly Contribution = pmt(8%/12,384,-12000,1714797.95)
Monthly Contribution = $ 879.89
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