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

Question

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

$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$?

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.

r = 100*  ?

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.

Kinshook · Accepted Answer

Given: 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.

Asked: When did the investor sell the bond if

r = 100*  ?

Monday: -
Purchase price of a bond = $p

After n number of days: - 
Value of the bond = $p (1+r%)^n

Next day:-
Value of the bond = $p (1+r%)^n - q
Selling price of the bond = $v
Since the investor sold the bond for market price,
$p (1+r%)^n - q = $v
p(1+r%)^n = v+q
(1+r%)^n = (v+q)/p
(1 + r%) = ((v+q)/p)^(1/n)
r% = (v+q)/p)^(1/n) - 1
r = 100* ((v+q)/p)^(1/n) - 1)

n=2 days

Investor sold the bond after 2+1 = 3 days

IMO B

chetan2u · Answer

A question that again fits in right for substituting values for variables.

Let us take  \frac{v+q}{p}=4 .
For this, let p=100, v=300 and q=100. =>  \frac{300+100}{100}=4.

r = 100* =100*(2-1)=100 %

So it doubles each day.

1) First day: 100 becomes 200
2) Second day: 200 becomes 400
3) Third day: 400 reduces by 100 and the bond is sold for 300.
Exactly as per the values taken.

B

Fdambro294 · Answer

(1st) we know that the initial value P is increasing by R% each day

Therefore we can express this daily increase in the Investment amount as:

P + (P) (r/100) ———> value after day 1

P * (1 + r/100)

The value after day 2 would be another multiplier = this r% increase or:

P * (1 + r/100) * (1 + r/100)

P * (1 + r/100)^2

Since there is a square root taken when we solve for r in terms of the other variables, 2 days of increases seem likely.

We can either continue down this path, subtract the -Q dollar increase on the 3rd day —— or —— we can back out the given equation.

(Principal) * (1 + percentage increase) - (Q dollar decrease on the last day) = Sales Price of V dollars

Step 1: divide 100 on both sides of equation

r/100 = sqrt( v + q / p) - 1

(r/100) + 1 = sqrt( v + q / p)

Step 2: now that we’ve isolated the Square Root, Square both sides of the equation

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

Step 3: multiple both sides by P = Principal amount

P * (1 + r/100)^2 = V + Q

Finally, subtract the Q dollars from both sides to set the equation equal to the final Sales dollar amount of V

P * (1 + r/100)^2 - Q = V

Since r/100 is the fractional form of the r% increase we can write)

P * (1 + r%) (1 + r%) - Q = V

What the given equation tells us is that the Principal had 2 time periods to increase its value by R% (each time period is a day ——> so 2 days)

And then on the 3rd day, the dollar value decreased by -Q dollars

This is equal to the final sales price of V dollars

3 days total

B

Posted from my mobile device

struggle_bus · Answer

Hi  Bunuel 
Would you be able to provide the solution step by step for this?

Thanks

chetan2u · Answer

I have given a method above that involves substitution and easier and faster method.

But if we have to do by algebra:-

Let the amount increase by r% for n days, and then it decreases by q next day to become v.
That is  v=p(1+\frac{r}{200})^n-q 
 v+q=p(1+\frac{r}{100})^n

Substitute in the value of r given by equation
 r = 100*  
so
 r = 100*  
 r/100=  
Let r/100 be a, so  a=(1+a)^{\frac{n}{2}}-1  or  a+1=(a+1)^{\frac{n}{2}} 
Thus, 1=n/2 or n=2

So it increased for 2 days and then dropped next day
Total days = 2+1 or 3 days.

bumpbot · Answer

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

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