Question 133960: A retired couple has $130,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $11,900 per year?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Interest(I) equals Principal(P) times Rate(R) times Time(T) or I=PRT
($ are understood)
Let P=amount invested in CD's @ 5%
Interest on this investment=P*0.05*1 or 0.05P
Then 130000-P=amount invested in AA bonds @ 11%
Interest on this investment=(130000-P)*0.11*1 or 0.11(130000-P)
Now we are told that the interest on these two investments needs to equal 11,900 so our equation to solve is:
0.05P+0.11(130,000-P)=11,900 simplify
0.05P+14,300-0.11P=11,900 subtract 14,300 from each side
0.05P+14,300-14,300-0.11P=11,900-14,300 collect like terms
-0.06P=-2400 divide both sides by -0.06
P=40,000 ------------amount invested on CD's at 5%
130,000-P=130,000-40,000=90,000------------amount invested in AA bonds at 11%
CK
40,000*0.05+90,000*0.11=11,900
2000+9900=11,900
11,900=11,900
Hope this helps---ptaylor
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