Question 90065: Could someone please help me in solving this problem, the answer I came up with was $25,759.
A financial advisor suggests to a client that she invest part of her portfolio in municipal bonds earning 6.5% annual simple interest, and the remainder in corporate bonds earning 8.5% interest. If she has $30,000 in her portfolio, how much should she be putting in the corporate bonds if she is to earn $2,190 in interest each year.
I have even tried solvers.
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A financial advisor suggests to a client that she invest part of her portfolio in municipal bonds earning 6.5% annual simple interest, and the remainder in corporate bonds earning 8.5% interest. If she has $30,000 in her portfolio, how much should she be putting in the corporate bonds if she is to earn $2,190 in interest each year.
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Let amount invested at 6.5% be "x"; interest on that is 0.065x dollars
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Amount invested at 8.5% is "30000-x"; interest on that is 0.085(30000-x)
= 2550 -0.085x dollars
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EQUATION:
interest + interest = 2190
0.065x + 2550 - 0.085x = 2190
-0.020x = -360
x= $18,000 (amt to be invested at 6.5%)
30000-x = $12000 (amt to be invested at 8.5%)
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Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! Let x = the amount to be invested in corporate bonds at 8.5% interest.
Then, ($30,000-x) would be invested in municipal bonds at 6.5% interest.
The total interest earned on these two investments is $2,190.
After changing the percentages to their equivalent decimal amounts (8.5% = 0.085 and 6.5% = 0.065), you can write the following equation:
x(0.085)+($30,000-x)(0.065) = $2,190 Simplify and solve for x.
0.085x+$1,950-0.065x = $2,190 Combine like-terms.
0.02x+$1,950 = $2,190 Subtract $1,950 from both sides.
0.02x = $240 Finally, divide both sides by 0.02
x = $12,000 This is the amount the client should invest in corporate bonds.
$30,000 - x = $30,000 - $12,000 = $18,000 is the amount the client would invest in municipal bonds.
Check:
(0.085)($12,000) + (0.065)($18,000) = $1,020 + $1,170 = $2,190 The total interest.
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