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An investor purchased a bond for p dollars on Monday. For a

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An investor purchased a bond for p dollars on Monday. For a [#permalink] New post 18 Jun 2006, 16:43
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if r = 100{[(v+q)/p]^1/2 - 1} ?

Wednesday of the same week.
Thursday of the same week.
Friday of the same week.
Monday of the next week.
Tuesday of the next week.


ANY IDEAS??!
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Re: DIFFICULT PERCENT PROBLEM [#permalink] New post 18 Jun 2006, 19:00
shehreenquayyum wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if r = 100{[(v+q)/p]^1/2 - 1} ?

Wednesday of the same week.
Thursday of the same week.
Friday of the same week.
Monday of the next week.
Tuesday of the next week.


initial price = p
price before decrease by q = p (1+r)^n
v = p (1+r)^n - q
v + q = p (1+r)^n


r = 100 {(v+q)/p)^1/2 - 1}

r = 100 [{p (1+r)^n /p}^1/2 - 1]

r = 100 [{(1+r)^n}^1/2 - 1]

now n should be 2. if n is 2 then, he sold the bond on Thursday of the same week.
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 [#permalink] New post 18 Jun 2006, 19:11
Increment is compounded because the increment each day is based on the increased rate from the previous day.

So

v = p(1 + r/100)^n - q where n is number of days (n is 1 day before q dollars drop)

{100[(v+q)/p - 1]}^ 1/n = r

We know n = 2, so he must have sold on Thursday because the drop only comes in n+1 days.
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 [#permalink] New post 18 Jun 2006, 23:33
Put n as the number of days. Calculate back and find that n = 2. The sale is made on the next day. This means three days transpired. So Thursday is the day on which he sold it.
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Thanks,
Zooroopa

  [#permalink] 18 Jun 2006, 23:33
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