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

3000 invested in stock A

2000 invested in stock B

Step-by-step 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`