# 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%.

(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)