You have already invested $300 in a stock with an annual return of 11%. How much of an additional $1,400

Question

You have already invested $300 in a stock with an annual return of 11%. How much of an additional $1,400 should be invested at 12% and how much at 6% so that the total return on the entire $1,700 is 9%? (Round each answer to the nearest cent.)

how much money at 12% 
how much money at 6%

Answer 1

For this type of problem, it's useful to make a table. Say x = the amount invested at 12%, which means that 1400 - x = the amount invested at 6% (we want them to add up to $1400 together). The first row in the table will represent the 11% stock, the second will represent the 12% stock, the third will represent the 6% stock, and the fourth will represent the overall investment:

 

INVESTMENT        INTEREST RATE        INTEREST ANNUALLY

300                                0.11                             0.11(300)

x                                      0.12                             0.12x

1400 - x                        0.06                              0.06(1400 - x)

1700                               0.09                              0.09(1700)

 

We want the annual interest from the first three rows to equal the interest target of the final investment. So, we can set up an equation and solve for x:

 

0.11(300) + 0.12x + 0.06(1400 - x) = 0.09(1700)

33 + 0.12x + 84 - 0.06x = 153

117 + 0.06x = 153

0.06x = 36

x = 600

 

So, x = $600 should be invested in the 12% stock and 1400 - 600 = $800 should be invested in the 6% stock.