Question

Jack has determined he will have an annual retirement income deficit. The deficit for the first year of retirement, 10 years from now, is $90,000. He expects to be in retirement for 30 years and believes he can earn a 7% after-tax annual return on invested dollars. Inflation is expected to average 4% annually over this same period. What is the amount of lump-sum retirement funds needed by Jack at the beginning of retirement to fund his additional retirement income needs? 1,816,961 1,790,644 1,392,409 1,842,297

Answer 1

Deficit for 1st year of retirement = 90000

Annual Inflation = 4% and After tax annual return = 7%, Retirement life = 30 years

Because of inflation deficit for each year will grow at 4% annually and at the same time lump fund in the retirement account will also grow at rate of 7% per year. To take both these effect into account we will calculate the real return and use it for calculating lump sum funds needed by Jack at beginning of retirement.

Real rate of return = [(1+ Annual after tax return) / ( 1 + Annual inflation)] - 1

= [(1+ 7%) / ( 1 + 4%)] - 1 = (1.07/1.04) - 1 = 1.028846154 - 1 = 0.028846154 = 2.8846154%

Amount of lump sum retirement fund needed by jack at the beginning of retirement will be equal present value of annuity of deficit discounted at real rate of return and can be calculated using pv function in excel.

Formula to be used in excel: =pv(rate,nper,-pmt,fv,type)

Here type = 1 as retirement income will be needed at beginning of the year and fv=0 as at the the end of 30 years amount in retirement fund will be 0

Using pv function we get lump sum fund needed at the beginning of retirement = 1842296.74 =1842297

Answer is 1842297