I plan to retire in 45 years. At his time I will be 70 years old. I expect to li

Question

I plan to retire in 45 years. At his time I will be 70 years old. I expect to live until I am 90. I believe I will need $120,000 per year to live once I retire. How much wealth will I need when I reach the age of 70? Assume a risk free rate of 6% for my retirement years. How much will I have to save beginning today if interest is paid at the end of each year and is compounded annually? Assume an investment rate of 4% from age 45 to retirement. (a) $53,264.22 (b) $44,868.48 (c) $42,868.48 (d) #52,868.48

Explanation / Answer

wealth neede when I reach the age of 70 = $120,000/1.03 +$120,000/1.03^2 + $120,000/1.03^3 .........................$120,000/1.03^20 =$1,785,296.98 let yearly savings be x $1,785,296.98 = x*(1+9%)^24 + x*(1+9%)^23 + x*(1+9%)^22..............x*(1+9%)^0 x= $21,077.66 (b) $21,077.66

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