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30 August, 08:49

Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A is 4% interest over 6 years. Plan B is 5% interest over 4 years. Using the formula m=P+Prt/12t for payment, m, which statement best compares the plans?

A. Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.

B. Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.

C. Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.

D. Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B.

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  1. 30 August, 09:08
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    Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B ⇒ answer B

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - Peter wants to borrow $3,000

    - He has two payment plans to choose from

    - Plane A: is 4% interest over 6 years

    - Plane B: is 5% interest over 4 years

    - The using formula is m = [P + Prt] / (12t), where m is the monthly

    payment, P is the money invested, r is the interest in decimal, and

    t is the time

    * Lets solve the problem

    # Plane A:

    ∵ P = $3000

    ∵ r = 4/100 = 0.04

    ∵ t = 6 years

    - The interest I = Prt

    ∴ I = 3000 * 0.04 * 6 = 720

    ∴ The total interest is $720

    - The monthly payment m = [P + Prt] / (12t)

    ∴ m = [3000 + 3000 * 0.04 * 6]/12 (6)

    ∴ m = [3000 + 720]/72

    ∴ m = [3720]/72 = 51.667

    ∴ The monthly payment is $51.667

    # Plane B:

    ∵ P = $3000

    ∵ r = 5/100 = 0.05

    ∵ t = 4 years

    - The interest I = Prt

    ∴ I = 3000 * 0.05 * 4 = 600

    ∴ The total interest is $600

    - The monthly payment m = [P + Prt] / (12t)

    ∴ m = [3000 + 3000 * 0.05 * 4]/12 (4)

    ∴ m = [3000 + 600]/48

    ∴ m = [3600]/48 = 75

    ∴ The monthly payment is $75

    - By comparing the two plans

    * The total interest of plan A is more than the total interest of plan B

    by $720 - $600 = $120

    * The monthly payment of plan A is less than the monthly payment

    of plan B by $75 - $51.667 = $23.33

    ∴ Plan A has a monthly payment of about $23 less and a total

    interest charge of $120 more than plan B
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