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

(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

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