SOLUTION: One safe investment pays 6​% per​ year, and a more risky investment pays 12​% per year. a. How much must be invested in each account if an investor of ​$102,000 would like

Algebra ->  College  -> Linear Algebra -> SOLUTION: One safe investment pays 6​% per​ year, and a more risky investment pays 12​% per year. a. How much must be invested in each account if an investor of ​$102,000 would like       Log On


   

Question 1202277: One safe investment pays 6​% per​ year, and a more risky investment pays 12​% per year. a. How much must be invested in each account if an investor of ​$102,000 would like a return of ​$7,800 per​ year? b. Why might the investor use two accounts rather than put all the money in the 12​% ​investment?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Part (a)

x = amount invested at 6%
102000-x = amount invested at 12%

0.06x = simple interest earned at 6% for one year
0.12(102000-x) = simple interest earned at 12% for one year

Add the two subtotals and set the sum equal to 7800. Solve for x.

0.06x+0.12(102000-x) = 7800
0.06x+0.12*102000+0.12*(-x) = 7800
0.06x+12240-0.12x = 7800
-0.06x+12240 = 7800
-0.06x = 7800-12240
-0.06x = -4440
x = -4440/(-0.06)
x = 74000

which leads to
102000-x = 102000-74000 = 28000


Answers:
$74,000 invested at 6%
$28,000 invested at 12%

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Part (b)

The 12% investment is more risky compared to the 6% investment. It's possible the 12% account could go to zero. You would lose all of your money if you put all of your eggs in one basket. It's better to diversify.