# Math

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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?

(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)

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