Stocks, Bonds, and CD Algebra Question

Question

Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks, bonds, and CDs. CDs pay 2.75 % interest, bonds pay 3.4 % interest, and stocks pay 11.6 % interest. Maricopa Success invests $ 20000 more in bonds than in CDs. If the annual income from the investments is $ 5732.5 , how much was invested in each account? 

Maricopa Success invested $     in stocks.

Maricopa Success invested $     in bonds. 

Maricopa Success invested $     in CDs. 

Answer 1

take the interest and divide by the investment to get the average interest rate

5,732.5/115= nearly 5% (4.9847826%)

round off the CD and B rates to about 3%

the stock rate is nearly 12%

about 4 times the investments will be in CDs and B's, with 1/5 left for stocks

5 is much closer to 3 than to 12.

CD's investment about $35,000

Bonds about $55,000

Stocks about $25,000

spend some tedious calculations to get closer numbers.

Answer 2

Lets say c in CDs

Then

c in CDs

20000 + c in bonds

115000 - c - (20000+c) in stocks = 95000 - 2c in stocks

Interest

CDs 2.75% of c = 0.0275c

Bonds 3.4% of (20000 + c) = 0.034 (20000 + c)

Stocks 11.6% of (95000 -2c) = 0.116 (95000 - 2c)

So 0.0275c + 0.034 (20000 +c) + 0.116 (95000-2c) = 5732.5

So you can solve this for c, then knowing c find out how much was invested in bonds and stocks