Question

You have already invested $550 in a stock with an annual return of 11%.  How much more should be invested at 15% so that the return on the total investment is 12%?

Answer 1

You need to invest $183.3 in a stock with an annual return of 15% so that the return on the total investment is 12%.

Explanation:

Consider the provided information.

You have already invested $550 in a stock with an annual return of 11%. The interest earn will be:
`550* (11)/(100)`

Let x amount invested at 15%, the interest earn will be:
`x* (15)/(100)`

It is given that we want that the return on the total investment is 12%

This can be written as

`550* (11)/(100) +x* (15)/(100)=(12)/(100)(x+550)`

Now solve the above equation for x.

`550* 0.11+x* 0.15=0.12(x+550)`

`60.5+0.15x=0.12x+66`

`0.15x-0.12x=66-60.5`

`0.03x=5.5`

`x=183.333..`

Hence, you need to invest $183.3 in a stock with an annual return of 15% so that the return on the total investment is 12%.

Answer 2

Solution: Let x be the amount to be invested (15%).

Then,

x*0.15 + 550*0.11 = (x+550)*0.12

x*0.15 - x*0.12 = 550*0.12 - 550*0.11

0.03x = 550*(0.12-0.11)

0.03x = 550*0.01

0.03x = 5.5

x =5.5÷0.03

x=183.33

Answer: $183.33 more to be invested for 12 % total return.