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One safe investment pays 8% per year, and a more risky investment pays 14% per year. a. How much must be invested in each account if an investor of $94,000 would like a return of $8,720 per year?

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Let amount invested at 8% per year = x

Let amount invested at 14% per year = y

Total investment is $94000 then we get equation:

x+y=94000

or

x=94000-y...(i)

Given that total return in 1 year is $8720 so we can write equation:

8% of x + 14% of y = 8720

or

0.08x+0.14y=8720...(ii)

plug (i) into (ii)

0.08(94000-y)+0.14y=8720

7520-0.08y+0.14y=8720

7520+0.06y=8720

0.06y=8720-7520

0.06y=1200

y=20000

plug value of y into (i)

x=94000-y=94000-20000=74000

Hence final answer is given by:

Amount invested at 8% per year = $74000

Amount invested at 14% per year = $20000


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