# Math

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Betsy, a recent retiree, requires \$6,000 per year in extra income. She has \$60,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 3% per year. How much money should be invested in each to realize exactly \$6,000 in interest per year?

The amount of money invested at 13%?

The amount of money invested at 3%?

• Math -

Investments:
x dollars @ 13%,
y dollars @ 3%,

x + y = 60000,
0.13x + 0.03y = 6000,
Multiply the 1st Eq by -0.13:
-0.13x - 0.13y = -7800,
0.13x + 0.03y = 6000,
Add the 2 Eqs:
-0.1y = -1800,
y = 18000,

Substitute 18000 for y in the 1st Eq:
x + 18000 = 60000,
x = 60000 - 18000 = 42000.

She invested:
\$42000 @ 13%,
\$18000 @ 3%.

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