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20 February, 01:02

Sarah's two student loans totaled $12,000. One of her loans was at 6% simple interest and the other at 3%. After one year, Sarah owed $585 in interest. What was the amount of each loan?

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  1. 20 February, 01:20
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    The loans are $4500 and $7500 respectively

    Step-by-step explanation:

    Let the principal amount of the two loans be x and y respectively.

    This means x + y = 12,000 (I)

    Now, for the first principal x, interest accrued will be

    I = PRT/100

    I = x * 6 * 1/100 = 6x/100

    For the second principal, interest accrued will be;

    I = y * 3 * 1/100 = 3y/100

    Since the total interest is $585

    That would be;

    6x/100 + 3y/100 = 585

    6x + 3y = 58500 (ii)

    Now we have two equations to solve simultaneously.

    Substitute x = 12,000 - y in equation ii

    6 (12000 - y) + 3y = 58,500

    72000 - 6y + 3y = 58500

    3y = 72000 - 58500

    3y = 13,500

    y = 13,500/3 = 4,500

    x = 12,000 - y = 12000 - 4500 = 7,500

    Hence the loan at 6% is 7,500 while the loan at 3% is 4,500
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