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

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Manager
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An investor purchased a bond for p dollars on Monday. For a [#permalink]  24 Aug 2006, 08:19
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)?

a. Wednesday of the same week.
b. Thursday of the same week.
c. Friday of the same week.
d. Monday of the next week.
e. Tuesday of the next week.

Notice i raised the problem above to the 1/2 because I am not sure how to put square root into this test.

i'll post the answer after a few replies...[/code]
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A.P.

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I got it by the following method:
monday morning price of bond = p
for the next n days, the price increased by r% each day. So basically the price got compounded (compound interest) on a daily basis.
Hence, at the end of n days, price of bond = p(1 + r/100)^n

on the n+1th day, price = [p(1 + r/100)^n] - q = v ( as given in the q)

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

Substituting this in the above eqn and solving, we get,
v = {(v+q)^n/2}/{p^(n/2-1)} - q --- (i)

also the choices given result in n having the value as 2,3,4,7 and 8 resp.
I chose the first answer and substituted 2 in eqn (i) and ... got the answ. ..

Alternate method:
for eqn (i) to hold true,
n/2 = 1 (so that q and q can cancel out); and
n/2 -1 = 0 so that the denominator in the first term reduces to 1.
from either of these eqns, you get n = 2. Hence answer is (A).

any OE ? what is the OA pls ?
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Prashrash.

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B

Not sure if this is correct, but when you square both sides, you'll get (1+r)^2 on the left side with some manipulation. This tells me interest was acrrued for two days. It was then sold the day after, so total 3 days. Three days from Monday is Thursday.
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agsfaltex wrote:
B

Not sure if this is correct, but when you square both sides, you'll get (1+r)^2 on the left side with some manipulation. This tells me interest was acrrued for two days. It was then sold the day after, so total 3 days. Three days from Monday is Thursday.

Agreed. So interest was accrued on monday and tuesday .. and it was sold on wednesday. hence it should be (A), shouldn't it ?
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Prashrash.

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you guys are genius's!!!! The answer is B

Here is the OA

We need to consider the formula for compound interest for this problem: F = P(1 + r)x, where F is the final value of the investment, P is the principle, r is the interest rate per compounding period as a decimal, and x is the number of compounding periods (NOTE: sometimes the formula is written in terms of the annual interest rate, the number of compounding periods per year and the number of years). Let's start by manipulating the given expression for r:

I attached the calculation
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File comment: Take a look at the picture for a better understanding

compound%20interest%20solution.gif [ 3.22 KiB | Viewed 608 times ]

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Re: Really hard problem- Problem solving [#permalink]  24 Aug 2006, 11:04
AshikaP 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)?

a. Wednesday of the same week.
b. Thursday of the same week.
c. Friday of the same week.
d. Monday of the next week.
e. Tuesday of the next week.

i did it before this way: http://www.gmatclub.com/phpbb/viewtopic ... light=bond
Re: Really hard problem- Problem solving   [#permalink] 24 Aug 2006, 11:04
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