Problema Solution
stock A is initially worth $1300 and loses $80 each month. stock B is initially worth $400 and gains 9.5% each month. when will stock B be worth more than stock A?
Answer provided by our tutors
Let 'x' represent the number of months.
After x months stock A will be worth: 1300 - 80x
After x months stock B will be worth: 400(1 + 0.95)^x
Stock B is worth more than stock A means:
400(1 + 0.95)^x > 1300 - 80x
400*1.95^x > 1300 - 80x divide both sides by 400
1.95^x > 13/4 + x/5
If we draw the graphs of:
y = 1.95^x
y = 13/4 + x/5
and look for the intersection we can find the answer.
We notice that for x > 2 the inequality 1.95^x > 13/4 + x/5 holds so after 2 months stock B will be worth more that stock A.
Indeed, for x = 2 we have:
Stock A will be worth: 1300 - 80x = 1300 - 2*80 = $1140
Stock B will be worth: 400(1 + 0.95)^2 = $1521