1. Challenge question. In the chapter text, we dealt exclusively with a single lump sum, but often we may be looking at several lump-sum values simultaneously. Let’s consider the retirement plan of a couple. Currently, the couple has four different investments: a 401(k) plan, two pension plans, and a personal portfolio. The couple is five years away from retirement. They believe they have sufficient money in their plans today so that they do not have to contribute to the plans over the next five years and will still meet their $2 million retirement goal. Here are the current values and growth rates of their plans:


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401(k): $88,000 growing at 6.5%


Pension plan 1: $304,000 growing at 7%


Pension plan 2: $214,000 growing at 7.25%


Personal portfolio: $149,000 growing at 8.5%


Does the couple have enough already invested to make their goal in five years?


Hint: View each payment as a separate problem, and find the future value of each lump sum five years from now. Then add up all the future values.


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