You have already invested $400 in a stock with an annual return of 11%. How much of an additional $1,200 should be invested at 12% and how much at 6% so that the total return on the entire $1,600 is 9%? (Round each answer to the nearest cent.)

Question

Mathematics

Tyson Shea

21 April, 21:09

You have already invested $400 in a stock with an annual return of 11%. How much of an additional $1,200 should be invested at 12% and how much at 6% so that the total return on the entire $1,600 is 9%? (Round each answer to the nearest cent.)

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Toby · Answer 1

The annual return on $400 in stock is 0.11*400 = $44

The total return you want is 0.09 * 1600 = $144

Let a be the amount invested at 12% and b be the amount invested at 6%

0.12a + 0.06b = 144 - 44

12a + 6b = 10000

a + b = 1200

Put those 2 equations together and solve for a and b:

12a + 6b = 10000

a + b = 1200

Using elimination, a = $466.67 and b = $733.33

So, out of an additional $1200, invest $466.67 at a rate of 12% and $733.33 at a rate of 6%