# 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?

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## Question:

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.

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

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– 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:

∵ r = 5/100 = 0.05

∵ t = 4 years

∴ I = 3000 × 0.05 × 4 = 600

The total interest is \$600

∴ 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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