Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 atonce. He puts a down payment of $14,000 for the boat and receives a loan for the rest of thepayment 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:Monthly payments=$418.14Total amount will be=down payment + 48×$418.14$14000+$20070.84=$34070.84Step-by-step explanation:Loan payment per month=Amount to pay÷discount factorMathematically  P=A÷Dwhere D is the discount factor calculated using the formula;[tex]\frac{(1+i)^n-1}{i(1+i)^n}[/tex]where i=periodic interest rate=annual rate divided by number of payment periodsA is the amount to pay after downpaymentP is the loan monthly payment amountn=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 paymentsGiven;Cost of boat=$32000Down payment=$14000Loan to pay=$32000-$14000=$18000Annual rate=5.5%=i=5.5%÷12=0.458%⇒0.00458Periodic payments, n=4×12=48Finding the discount factor D;[tex]D=\frac{(1+i)^n-1}{i(1+i)^n} \\\\\\D=\frac{(1+0.00458)^{48} -1}{0.00458(1+0.00458)^{48} } \\\\\\D=\frac{1.2455-1}{0.005703} \\\\\\D=\frac{0.2455}{0.005703} =43.05[/tex]To get the amount to pay monthly divide the loan to pay with the discount factor[tex]=\frac{18000}{43.05} =418.14[/tex]Monthly payments=$418.14Total amount will be=down payment + 48×$418.14$14000+$20070.84=$34070.84