Question

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?

Answer 1

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

Explanation:

Loan payment per month=Amount to pay÷discount factor

Mathematically P=A÷D

where D is the discount factor calculated using the formula;

`((1+i)^n-1)/(i(1+i)^n)`

where i=periodic interest rate=annual rate divided by number of payment periods

A is the amount to pay after downpayment

P is the loan monthly payment amount

n=number of periodic payments=payments per year times number of years

⇒In this question you find the discount factor then divide the amount remaining to pay with the discount factor to get monthly payments

Given;

Cost of boat=$32000

Down payment=$14000

Loan to pay=$32000-$14000=$18000

Annual rate=5.5%=i=5.5%÷12=0.458%⇒0.00458

Periodic payments, n=4×12=48

Finding the discount factor D;

`D=((1+i)^n-1)/(i(1+i)^n) \\\\\\D=((1+0.00458)^(48) -1)/(0.00458(1+0.00458)^(48) ) \\\\\\D=(1.2455-1)/(0.005703) \\\\\\D=(0.2455)/(0.005703) =43.05`

To get the amount to pay monthly divide the loan to pay with the discount factor

`=(18000)/(43.05) =418.14`

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84