SOLUTION: a retired couple has 170,000 to invest to obtain annual income. they want some of it investing in safe certificstes of deposit yielding 5 percent. the rest they want to invest in A

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Question 424851: a retired couple has 170,000 to invest to obtain annual income. they want some of it investing in safe certificstes of deposit yielding 5 percent. the rest they want to invest in AA bonds yielding 11% per year. how much should they invest in each to exactly 15,700 per year?
Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount invested @ 5%
Let b = amount invested @ 11%
given:
(1) a+%2B+b+=+170000
(2) +.05a+%2B+.11b+=+15700+
----------------------
Multiply both sides of (2) by 100
Multiply both sides of (1) by 5
and subtract (1) from (2)
(2) +5a+%2B+11b+=+1570000+
(1) +-5a+-+5b+=+-850000+
+6b+=+720000+
+b+=+120000+
and, since
(1) a+%2B+120000+=+170000
a+=+50000+
$50,000 = amount invested @ 5%
$120,000 = amount invested @ 11%

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
AA 11.00% per annum------------- x
CD 5.00% per annum------------ y
total investment 170000
Interest-----$15,700.00
......
x+y=170000 ------------------------1
11.00%x+5.00%y=$15,700.00
Multiply by 100
11x+5y=$1,570,000.00

Multiply (1) by -11
we get

-11x-11y=-1870000

Add this to (2)

-6y=-$300,000.00
divide by -6
y=$50,000.00
Balance $120,000.00