Question

You invest $ 5000 in two stocks . In one year , the value of stock A increases by 5.2 % and the value of stock B increases by 12.8 % The total value of the stocks is now $ 5412 . How much did you originally invest in each stock ?
Stock A=
Stock B=

Answer 1

Answer:

3000 invested in stock A

2000 invested in stock B

Explanation:

Given

$r_A = 5.2\%$ --- rate of stock A

$r_B = 12.8\%$ --- rate of stock B

$A = 5000$ --- Amount invested

$Total = 5412$ ---- Value of stock

Required

Determine the amount invested in each

Let

$x \to$ Amount invested in A

$y \to$ Amount invested in B

So:

$x + y = A$

$x + y = 5000$

Make x the subject

$x = 5000- y$

The gain on stock A is:

$A_{New} = x * r_A$

$A_{New} = (5000 - y) * 5.2\%$

$A_{New} = (5000 - y) * 0.052$

$A_{New} = 260 - 0.052y$

The gain on stock B is:

$B_{New} = y * r_B$

$B_{New} = y* 12.8\%$

$B_{New} = y* 0.128$

$B_{New} = 0.128y$

So, we have:

$A_{New} + B_{New} = Total - A$ ----- i.e. total gain on both stocks

$260 -0.052y+0.128y = 5412 -5000$

$260 -0.052y+0.128y = 412$

Collect like terms

$-0.052y+0.128y = 412-260$

$0.076y = 152$

Solve for y

$y = 2000$

To solve for x, we have:

$x = 5000- y$

$x = 5000 - 2000$

$x = 3000$