A retired couple needs $12,000 per year in income to supplement their Social Security. They have $150,000 to invest to obtain this income. They have decided on two investment options: AA bonds yielding 10% per annum and a bank CD yielding 5%.

Question

(a) How much should be invested in each to realize exactly $12,000 in interest income?
(b) If, after two years, the couple requires $14,000 per year in income, how should they reallocate their investment to achieve the new amount?

can you show me how you got your answer please?

(a) Let x be the amount invested in AA binds and y be the amount invested in CDs. You have two equations in two unknowns. They are
x + y = 150,000 (total principal available)
0.1 x + 0.05 y = 12,000 (desired income)
Now do the algebra.
x + 0.5 y = 120,000 (second equation x2)
0.5 y = 30,000. (subracting last equation from first)
y = 60,000. (doubling last equation)
x = 60,000.

(b) Use a similar procedure here, but the equations are:
x + y = 150,000 (total principal available)
0.1 x + 0.05 y = 14,000 (desired income)

Answer 1

Correct answers are:
A.) x= 90,000 & y= 60,000
B.) x= 130,000 & y= 20,000

Answer 2

to think this was 14 years ago...

Answer 3

sorry if I'm 14 years late but the answer is
A.) x= 90,000 & y= 60,000
B.) x= 130,000 & y= 20,000
and this was also made the year I was born

Answer 4

And no one even answered until 8 year later!

Answer 5

Damn, no one even showed how they got their answer. Which, I suppose, doesn't matter all that much anyway since the fastest reply to the question happened to be 8 years after the question had been asked. The questioner was probably already in a job by then lol.

Answer 6

Yes, it's unfortunate that no one showed their work or provided an explanation for their answers. However, it's never too late to learn and understand the solution!