your sister turned 35 today, and she is planning to save $7000 per year for reti

Question

your sister turned 35 today, and she is planning to save $7000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 30. Under these assumptions, how much can she spend each year after she tires? Her first withdrawal will be make at the end of her first retirement year

Explanation / Answer

FV at the time of retirement

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

     = 7000 x [((1 + 0.075)30 -1)/0.075]

FV = 723795

Now , we can calculate her annual withdrawal

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

723795 = PMT [(1 - (1 / (1 +0.075)-25)) / 0.075]

PMT = 723795 /  [(1 - (1 / (1 +0.075)-25)) / 0.075]

        = 64932

SO ANNUAL WITHDRAWAL WILL BE 64932 PER ANNUM

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