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Question 624588: You have already invested $450 in a stock with an annual return of 11%. How much of an additional $800 should be invested at 12% and how much at 6% so that the total return on the entire $1,250 is 9%? (Round each answer to the nearest cent.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! original investment = 450 with annual return of 11%.
add $800, some at 12% and some at 6%.
total return on entire $1250 equals 9%.
assume x at 12% and assume 800-x at 6%
sum of all investment is equal to 800 + 450 = 1250
total interest = 1250 * .09
your formula is:
.11*450 + .12*x + .06(800-x) = .09*1250
simplify to get:
.11*450 + .12*x + .06*800 - .06*x = .09*1250
simplify further to get:
49.5 + .12*x + 48 - .06*x = 112.5
combine like terms to get:
97.5 + .06*x = 112.5
subtract 97.5 from both sides of the equation to get:
.06*x = 112.5 - 97.5 which simplifies to:
.06*x = 15
divide both sides by .06 to get:
x = 15/.06 which simplifies to:
x = 250
when x = 250, 800 - x = 550
your formula of:
.11*450 + .12*x + .06(800-x) = .09*1250 becomes:
.11*450 + .12*250 + .06*550 = .09*1250 which simplifies to:
49.5 + 30 + 33 = 112.5
combine like terms to get:
112.5 = 112.5
this confirms the results of x = 250 and 800-x = 550 as good.
you need to invest 450 at 11% and 250 at 12% and 550 at 6% and you'll get a total combined interest rate of .09 on the total of 1250.
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