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29 August, 13:26

Laura owes $18,000 on her student loans. The interest rate on the bank loan is 2.5% and the interest rate on the federal loan is 6.9%. The total amount of interest she paid last year was $1,066. What was the principal for each loan?

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  1. 29 August, 14:05
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    The principal of the bank loan is $4,000

    The principal of the federal lone is $14,000

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - Laura owes $18,000 on her student loans

    - The interest rate on the bank loan is 2.5%

    - The interest rate on the federal loan is 6.9%

    - The total amount of interest she paid last year was $1,066

    * Assume that the principle of the bank loan is $x and The principal of

    the federal loan is $y

    ∵ Her loan is 18,000

    ∴ x + y = 18,000 ⇒ (1)

    - The interest is I = PRT, where P is the principal, R is the rate of interest

    in decimal ant is the time

    # The bank lone

    ∵ P = $x

    ∵ R = 2.5/100 = 0.025

    ∵ T = 1

    ∴ The interest of the bank lone = x (0.025) (1) = 0.025 x

    # The federal lone

    ∵ P = $y

    ∵ R = 6.9/100 = 0.069

    ∵ T = 1

    ∴ The interest of the federal lone = 9 (0.069) (1) = 0.069 y

    - The total interest is the sum of the interest of the bank lone and the

    interest of the federal loan

    ∵ The total interest is $1,066

    ∴ 0.025 x + 0.069 y = 1,066 ⇒ (2)

    * We have system of equations

    - Multiply equation (1) by - 0.025 to eliminate x

    ∴ - 0.025 x - 0.025 y = - 450 ⇒ (3)

    - Add equations (2) and (3)

    ∴ 0.044 y = 616

    - Divide both sides by 0.044

    ∴ y = 14,000

    - Substitute value of y in equation (1) to find x

    ∴ x + 14000 = 18000

    - Subtract 18000 from both sides

    ∴ x = 4000

    ∵ x represents the principal of the bake loan and y represents the

    principal of the federal lone

    * The principal of the bank loan is $4,000

    * The principal of the federal lone is $14,000
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