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

- 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