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=

Answers

Answer 1

Answer:

3000 invested in stock A

2000 invested in stock B

Explanation:

Given

[tex]r_A = 5.2\%[/tex] --- rate of stock A

[tex]r_B = 12.8\%[/tex] --- rate of stock B

[tex]A = 5000[/tex] --- Amount invested

[tex]Total = 5412[/tex] ---- Value of stock

Required

Determine the amount invested in each

Let

[tex]x \to[/tex] Amount invested in A

[tex]y \to[/tex] Amount invested in B

So:

[tex]x + y = A[/tex]

[tex]x + y = 5000[/tex]

Make x the subject

[tex]x = 5000- y[/tex]

The gain on stock A is:

[tex]A_{New} = x * r_A[/tex]

[tex]A_{New} = (5000 - y) * 5.2\%[/tex]

[tex]A_{New} = (5000 - y) * 0.052[/tex]

[tex]A_{New} = 260 - 0.052y[/tex]

The gain on stock B is:

[tex]B_{New} = y * r_B[/tex]

[tex]B_{New} = y* 12.8\%[/tex]

[tex]B_{New} = y* 0.128[/tex]

[tex]B_{New} = 0.128y[/tex]

So, we have:

[tex]A_{New} + B_{New} = Total - A[/tex] ----- i.e. total gain on both stocks

[tex]260 -0.052y+0.128y = 5412 -5000[/tex]

[tex]260 -0.052y+0.128y = 412[/tex]

Collect like terms

[tex]-0.052y+0.128y = 412-260[/tex]

[tex]0.076y = 152[/tex]

Solve for y

[tex]y = 2000[/tex]

To solve for x, we have:

[tex]x = 5000- y[/tex]

[tex]x = 5000 - 2000[/tex]

[tex]x = 3000[/tex]


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