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# An investor purchased a share of non-dividend-paying stock

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Intern
Joined: 10 Feb 2007
Posts: 33
An investor purchased a share of non-dividend-paying stock  [#permalink]

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14 Apr 2007, 17:55
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31
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Difficulty:

95% (hard)

Question Stats:

45% (02:41) correct 55% (03:00) wrong based on 294 sessions

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An investor purchased a share of non-dividend-paying stock for p dollars on Monday. For a certain number of days, the value of the share increased by r percent per day. After this period of constant increase, the value of the share decreased the next day by q dollars and the investor decided to sell the share at the end of that day for v dollars, which was the value of the share at that time. How many working days after the investor bought the share was the share sold, if $$r=100(\sqrt{\frac{v+q}{p}}-1)$$

A. Two working days later.
B. Three working days later.
C. Four working days later.
D. Five working days later.
E. Six working days later.
Manager
Joined: 01 Jan 2007
Posts: 226
Re: Another 700 level Question - Percents  [#permalink]

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15 Apr 2007, 23:54
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3
Witchiegrlie wrote:
An investor purchased a share of non-dividend-paying stock for p dollars on Monday. For a certain number of days, the value of the share increased by r percent per day. After this period of constant increase, the value of the share decreased the next day by q dollars and the investor decided to sell the share at the end of that day for v dollars, which was the value of the share at that time. How many working days after the investor bought the share was the share sold, if
(see image)

Two working days later.
Three working days later.
Four working days later.
Five working days later.
Six working days later.

Okay let d=total no. of days for which the price of the stock increases at r% a day.

Now form the question stem we can make the following equation.

v= p [1 + r/100]^d - q
there fore (v+q)/p = [ 1 + r/100 ]
But form the question stem we have r= 100 [ sqrt [ ( v+q)/p] ]
Therefore (v+q)/p= ( 1+ r/100)^d=( r/100 +1)^2

Therefore d=2. So the trader sold the stock after 2+1= 3 days.

Javed.

Cheers!
##### General Discussion
Director
Joined: 09 Aug 2006
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06 Oct 2007, 06:16
3
1
singh_amit19 wrote:
An investor purchased a share of non-dividend-paying stock for p dollars on Monday. For a certain number of days, the value of the share increased by r percent per day. After this period of constant increase, the value of the share decreased the next day by q dollars and the investor decided to sell the share at the end of that day for v dollars, which was the value of the share at that time. How many working days after the investor bought the share was the share sold, if r= 100 X [sqrt(v+q)/p)-1] ?

A. Two working days later.
B. Three working days later.
C. Four working days later.
D. Five working days later.
E. Six working days later.

B.

Formula for compound interest:
Final Value = P (1 + r/100)^t

In our question:
P = p
r = r
Final Value = v
number of days of compounding is unknown.

Given: r= 100 X [sqrt(v+q)/p)-1]

r/100 = [sqrt [(v + q)/p]] - 1
1 + r/100 = sqrt [(v + q)/p]
(1 + r/100)^2 = (v + q)/p
p (1 + r/100) ^2 = v + q
v = p (1 + r/100)^2 - q

This is in the same form as the formula for compound interest with the exception of '-q'. But from the question stem, we can infer that the negative q, refers to the decrease in the value of the stock. So, the initial value p compounded for 2 days (r = 2) and fell by q dollars on the third day ('next day' as stated in the stem). So the investor sold the stock on the third day.

I came across this question before and couldn't solve it then, which is why I know the solution this time round
Manager
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Re: An investor purchased a share of non-dividend-paying stock  [#permalink]

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20 Feb 2012, 06:05
3
1
$$v = p (1 + \frac{r}{100})^n - q$$

$$r = 100\sqrt{\frac{v+q}{p}} -1$$

$$v+q = p(\sqrt{\frac{v+q}{p}})^n$$

$$p^n^/^2(v+q) = p(v+q)^n^/^2$$

$$n = 2$$

so, the value increased for two days and the investor sold the third day, the same day when the price fell.
ans: b
Manager
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29 Apr 2007, 02:02
2
B) 3 days

- the price increased by r/100 per day over 'x' days -> p * [1+(r/100)]^x
- the price was reduced by 'q' on day 'x+1' -> p * [1+(r/100)]^x - q
- the selling price was 'v' -> v = p * [1+(r/100)]^x - q

v+q/p = [1+(r/100)]^x
if we compare the above formula with the one given, we will note that x=2, therefore this person sold the share in day x+1 = 3 days later.
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Re: An investor purchased a share of non-dividend-paying stock  [#permalink]

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05 Aug 2017, 06:20
2
1
Apologies for posting a screenshot.I tried to write everything down in comments but messed up the formulas.
Attachments

File comment: Solution

image.jpg [ 1.27 MiB | Viewed 6200 times ]

Retired Moderator
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Re: An investor purchased a share of non dividend paying stock  [#permalink]

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17 Mar 2011, 07:38
1
1
r% per day = 365r % per annum = 3.65r

Original equation is;
$$FV=PV(1+\frac{r}{n})^{nt}$$

Here
PV=p
FV=v
r = rate of interest per annum = 365r% = 3.65r
n=periods or frequency with which the rate is applied=365(the rate is applied daily; thus making the frequency per year as 365)
t= time in years= d days = d/365 years
The equation then would look something like this;

$$v = p(1+3.65r)^{(\frac{d}{365}*{365})}-q$$ ### -q is the extra bit because after the money value increased for d days; it plummeted by $q on the last day "(d+1st) day". $$v = p(1+\frac{3.65r}{365})^{d}-q$$ $$v = p(1+\frac{r}{100})^{d}-q$$ Now, try substituting for r; $$r = 100(\sqrt{\frac{v+q}{p}}-1)$$ $$v = p[1+\frac{100(\sqrt{\frac{v+q}{p}}-1)}{100}]^{d}-q$$ $$v = p[1+\sqrt{\frac{v+q}{p}}-1]^{d}-q$$ $$v = p(\sqrt{\frac{v+q}{p}})^{d}-q$$ $$\frac{v+q}{p} = (\sqrt{\frac{v+q}{p}})^{d}$$ Let $$\frac{v+q}{p}$$ be $$\Delta$$ $$\Delta^1 = \sqrt{\Delta}^{d}$$ Squaring both sides $$\Delta^2 = \Delta^{d}$$ d=2 Thus he sold the stock on d+1 = 2+1 = 3 days AnkitK, could you please correct the question? Director Joined: 23 Jan 2013 Posts: 521 Schools: Cambridge'16 Re: An investor purchased a share of non-dividend-paying stock [#permalink] ### Show Tags 26 Oct 2015, 00:50 1 Monday: P Tuesday: p(1+r/100) Wednesday: p(1+r/100)^2 Thursday: p(1+r/100)^3 we have square root in the definition of r, so it was the second day of increase + one day of decrease B Intern Joined: 01 Dec 2007 Posts: 23 ### Show Tags 08 Dec 2007, 11:23 1 querio wrote: B) 3 days - the price increased by r/100 per day over 'x' days -> p * [1+(r/100)]^x - the price was reduced by 'q' on day 'x+1' -> p * [1+(r/100)]^x - q - the selling price was 'v' -> v = p * [1+(r/100)]^x - q v+q/p = [1+(r/100)]^x if we compare the above formula with the one given, we will note that x=2, therefore this person sold the share in day x+1 = 3 days later. So the trick is to know the interest compounding formula and set it equal to V. Manager Joined: 11 Feb 2011 Posts: 105 An investor purchased a share of non dividend paying stock [#permalink] ### Show Tags Updated on: 17 Mar 2011, 08:48 1 An investor purchased a share of non dividend paying stock for p dollars on monday.For a certain number of days the value of share increased by r % per day.After this period of constant increase,the value of shARE decreased the next day by q dollars and the investors decided to sell the share at the end of that day for v dollars ,which was the value of the share at that time.How many working days after the investor bought the share was the share sold if r=(100[(v+q)/p]^1/2-1) A.2 working days later B.2 working days later C.4 working days later D.5 working days later E.6 working days later Originally posted by AnkitK on 17 Mar 2011, 05:59. Last edited by AnkitK on 17 Mar 2011, 08:48, edited 1 time in total. Manager Joined: 18 Oct 2010 Posts: 61 Re: An investor purchased a share of non dividend paying stock [#permalink] ### Show Tags 17 Mar 2011, 20:29 it takes maybe about 2.30 mins to make a count if you know about future value and present value in finacial stuff.... future value is FV as fluke said present value is PV and r is interest for sure the formula is FV=PV(1+r%)^n (n is number of period) here you dont need to divide by 365 days or 360 days, because r in the question is counted by days as the question said ( 360 days or 365 days is decided by banks to count interest..so we dont care about it) . Thus we will have the fomula like P- present value, future value is V and r is know P*{{1+100*([(r+q)/100p]^1/2)-1}^n}-q=v ( we have to minus q because after n+1 day the future value will be decreased by q and we have to divide by 100 because its r% ok? <=> p*{(r+q)/p}^1/2}^n=v+q or {[(r+q)/p]^1/2}=(v+q)/P here we see that only n=2 works with the above formular Intern Joined: 17 Mar 2011 Posts: 9 Re: An investor purchased a share of non dividend paying stock [#permalink] ### Show Tags 17 Mar 2011, 20:51 Simpler quicker approach. Look at the equation given. v+q is the price before the final drop. Divided by p you have the total multiplier of the stock price's increase. This is the %increase for one 'term' if you subtract 1. But it is ^(1/2) which means you are looking at two terms, and since the question tells us that r% refers to 1 day, then 2 terms is 2 days. Just remember to add 1 at the end for the day it decreased, and=3. Manager Joined: 11 Feb 2011 Posts: 105 Re: An investor purchased a share of non dividend paying stock [#permalink] ### Show Tags 17 Mar 2011, 21:55 Dear Boston,pls explain the meaning of the statement more precisely " But it is ^(1/2) which means you are looking at two terms, and since the question tells us that r% refers to 1 day, then 2 terms is 2 days. " Still not clear Intern Joined: 17 Mar 2011 Posts: 9 Re: An investor purchased a share of non dividend paying stock [#permalink] ### Show Tags 17 Mar 2011, 22:43 If the total multiplier from inital price (I) to end price (E) is 'x', i.e. E=Ix, then: for one period of price changes, the period multiplier (1+%r in this problem) will be equal to the total multiplier, =x. for two periods, the period multiplier will be the square root of x since the I will be multiplied twice by it to reach E. for n periods, the period multiplier (1+%r) will be the nth root of x. I dont like the formula used above re: /365 and per annum etc, because the question's period could have referred to e.g. seconds instead of days and we dont really want to be turning seconds into per annum.. Intern Joined: 17 Sep 2016 Posts: 3 Re: An investor purchased a share of non-dividend-paying stock [#permalink] ### Show Tags 26 Oct 2016, 00:44 I have a small doubt, how do we identify whether we solve it using Simple interest or compound interest Intern Joined: 03 Jun 2017 Posts: 10 Re: An investor purchased a share of non-dividend-paying stock [#permalink] ### Show Tags 23 Jun 2017, 22:31 Hi: Kindly explain, how we decided to use Compound interest formula? Thanks in advance Director Joined: 12 Nov 2016 Posts: 692 Location: United States Schools: Yale '18 GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66 Re: An investor purchased a share of non-dividend-paying stock [#permalink] ### Show Tags 24 Jun 2017, 03:18 Witchiegrlie wrote: An investor purchased a share of non-dividend-paying stock for p dollars on Monday. For a certain number of days, the value of the share increased by r percent per day. After this period of constant increase, the value of the share decreased the next day by q dollars and the investor decided to sell the share at the end of that day for v dollars, which was the value of the share at that time. How many working days after the investor bought the share was the share sold, if $$r=100(\sqrt{\frac{v+q}{p}}-1)$$ A. Two working days later. B. Three working days later. C. Four working days later. D. Five working days later. E. Six working days later. Simple- we can deconstruct this problem by constructing variables- so let p =$2
Q=$12 V=$60

R= 100(\sqrt{60 + 12/2}-1_
R= 100(5)
R= 500 percent

So if the stock was initially bought at $2 dollars on day 1 then it had increased to$12 dollars on day 2 and then 72\$ on the third day which is the day it was sold - three days.

Thus
"B"
Intern
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Re: An investor purchased a share of non-dividend-paying stock  [#permalink]

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31 Oct 2017, 03:03
Please explain, how we decided to use Compound interest formula?

Posted from my mobile device
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Re: An investor purchased a share of non-dividend-paying stock  [#permalink]

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31 Oct 2017, 09:05
[quote="shreya1018"]Please explain, how we decided to use Compound interest formula?

shreya1018 : I am happy to respond, We have to use CI because in the question it mentioned "For a certain number of days, the value of the share increased by r percent per day"

Everyday it was increasing by r%

So initially if the investor had P.
1st Day : P + r% of P
2nd Day : (P + r% of P) + r% of ( P + r% of P) and so on...

This is exactly what Compound Interest is.So,we used CI formula and not SI.
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Re: An investor purchased a share of non-dividend-paying stock  [#permalink]

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