Answer:
Monthly payments=$418.14
Total amount will be=down payment + 48×$418.14
$14000+$20070.84=$34070.84
Step-by-step explanation:
Loan payment per month=Amount to pay÷discount factor
Mathematically P=A÷D
where D is the discount factor calculated using the formula;
![\frac{(1+i)^n-1}{i(1+i)^n}](https://tex.z-dn.net/?f=%5Cfrac%7B%281%2Bi%29%5En-1%7D%7Bi%281%2Bi%29%5En%7D)
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=\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](https://tex.z-dn.net/?f=D%3D%5Cfrac%7B%281%2Bi%29%5En-1%7D%7Bi%281%2Bi%29%5En%7D%20%5C%5C%5C%5C%5C%5CD%3D%5Cfrac%7B%281%2B0.00458%29%5E%7B48%7D%20-1%7D%7B0.00458%281%2B0.00458%29%5E%7B48%7D%20%7D%20%5C%5C%5C%5C%5C%5CD%3D%5Cfrac%7B1.2455-1%7D%7B0.005703%7D%20%5C%5C%5C%5C%5C%5CD%3D%5Cfrac%7B0.2455%7D%7B0.005703%7D%20%3D43.05)
To get the amount to pay monthly divide the loan to pay with the discount factor
![=\frac{18000}{43.05} =418.14](https://tex.z-dn.net/?f=%3D%5Cfrac%7B18000%7D%7B43.05%7D%20%3D418.14)
Monthly payments=$418.14
Total amount will be=down payment + 48×$418.14
$14000+$20070.84=$34070.84