Question 32274
Hello!
Let's call X to the additional amount he must invest. The total interest received from both investments will be {{{11000*0.12 + X*0.15}}} (12% of the $11,000 and 15% of the $X). Also, he wants his average return to be 13%. This means that his total interest should be {{{(11000+X)*0.13}}} (13% on the total invested amount). Since he wants both this expression to be equal, we get the equation:

{{{(11000+X)*0.13 = 11000*0.12 + X*0.15}}}

And now we just isolate X:

{{{11000*0.13 + X*0.13 = 11000*0.12 + X*0.15}}}
{{{1430 + X*0.13 = 1320 + X*0.15}}} 
{{{1430 - 1320 = X*0.15 - X*0.13 }}}
{{{ 110 = X*0.02}}}
{{{X = 110/0.02 = 5500}}}

We conclude that he should invest an additional $5,500 in the 15% account.


I hope this helps!
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