Answer:
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
