Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at once. he puts a down payment of $14,000 for the boat and receives a loan for the rest of the payment of the boat. the loan has an interest rate of 5.5% and is to be paid out over 4 years. what is henry’s monthly payment, and how much does he end up paying for the boat overall? ( show steps) : )

Henry's monthly payment is $457.5

Henry pays up for the boat at the end overall $35,960

Step-by-step explanation:

* Lets explain how to solve the problem

- Henry buys a large boat with full amount of $32,000

- He cannot pay the full amount at once

- He puts a down payment of $14,000

- He receives a loan for the rest of the payment

∵ The rest of payment = 32,000 - 14,000 = $18,000

- The loan has an interest rate of 5.5%

∴ The rate of interest = 5.5/100 = 0.055

- It is to be paid out over 4 years

∵ The amount of interest = P × r × t , where

# P is the principle amount

# r is the rate

# t is the time

∵ P = 18, 000 , r = 0.055 , t = 4

∴ The amount of interest = 18,000 × 0.055 × 4 = $3960

- The total remaining amount is the sum of the rest of payment and

 the amount of interest

∵ The rest of payment is $18,000

∵ The interest amount = $3,960

∴ The total remaining amount = 18,000 + 3,960 = $21960

- The number of monthly payments = 12 × t

∵ t = 4

∴ The number of monthly payment = 12 × 4 = 48 months

- The monthly payment = the total remaining ÷ the number of

  monthly payment

∵ The total remaining is 21960

∵ The number of monthly payment = 48

∴ The monthly payment = 21960 ÷ 48 = $457.5

* Henry's monthly payment is $457.5

- The total paying for the boat is the sum of the payment down and

  the remaining total payment

∵ The payment down is $14,000

∵ The remaining total payment is 21,960

∴ The total payment for the boat = 14,000 + 21,960 = $35,960

* Henry pays up for the boat at the end overall $35,960