Math

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%?

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  1. 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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