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â(Future valueâ) Sarah Wiggum would like to make a singleâ lump-sum investment and have â$ 1.7 million at the time of her retirement in 34 years. She has found a mutual fund that expects to earn 8 percent annually. How much must Sarah investâ today? If Sarah earned an annual return of 16 16 âpercent, how much must she investâ today? a. If Sarah can earn 8 percent annually for the next 34 âyears, how much will she have to investâ today? â $ nothing â(Round to the nearestâ cent.)

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sqdancefan

Answer:

  a) at 16%: $10,936.47

  b) at 8%: $124,177.02

Step-by-step explanation:

At annual rate of return "r", the multiplier of Sarah's initial investment will be ...

  k = (1+r)^34

For r = 0.16, k ≈ 155.433166, and Sarah's investment needs to be ...

  $1.7·10^6/k ≈ $10,936.47

__

For r= 0.08, k ≈ 13.6901336, and Sarah's investment needs to be ...

  $1.7·10^6/k ≈ $124,177.02

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