anthony has decided to purchase a $19000 car. he plans to put 20% down toward the purchase and to finance the rest at a 6.8% interest rate for 4 years. find the monthly payment
balance of loan = .8(19000) = 15200
monthly rate = i = .068/12
n = 12(4) = 48
payment --- p
solve for p,
p(1 - (1+i)^-48 )/i = 15200
To find the monthly payment for the car loan, you can use the formula for calculating the monthly payment on an amortized loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = Monthly payment
P = Principal amount (loan amount)
i = Monthly interest rate
n = Total number of monthly payments
Let's calculate each component step-by-step.
Step 1: Calculate the loan amount (principal amount)
The car's purchase price is $19,000, and Anthony plans to put 20% down. So the loan amount (principal amount) can be calculated as:
Loan amount = $19,000 - (20% of $19,000)
= $19,000 - (0.20 x $19,000)
= $19,000 - $3,800
= $15,200
Step 2: Calculate the monthly interest rate
The annual interest rate is given as 6.8%. We need to convert it into a monthly interest rate:
Monthly interest rate = Annual interest rate / 12
= 6.8% / 12
= 0.068 / 12
= 0.00567
Step 3: Calculate the total number of monthly payments
Anthony plans to finance the car for 4 years, or 48 months. Therefore, the total number of monthly payments (n) is 48.
Step 4: Calculate the monthly payment
Now, we can substitute the values into the formula and calculate the monthly payment (M):
M = $15,200 [ 0.00567(1 + 0.00567)^48 ] / [ (1 + 0.00567)^48 - 1 ]
Using a calculator or spreadsheet software, you can calculate the monthly payment to be:
M ≈ $354.60
Therefore, the approximate monthly payment for Anthony's car loan is $354.60.
To find the monthly payment for the car loan, we can use the formula for calculating the monthly payment for a fixed-rate loan:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Number of Months))
First, let's calculate the loan amount. Anthony plans to put 20% down toward the purchase, so the down payment amount will be:
Down Payment = 20% * $19000 = $3800
The loan amount will be the remaining purchase price after the down payment:
Loan Amount = $19000 - $3800 = $15200
Next, we need to calculate the monthly interest rate. The annual interest rate is given as 6.8%. To convert it into a monthly interest rate, we divide it by 12 (the number of months in a year) and then convert it to a decimal:
Monthly Interest Rate = 6.8% / 12 / 100 = 0.00567
Now, we can calculate the monthly payment using the formula above:
Monthly Payment = ($15200 * 0.00567) / (1 - (1 + 0.00567) ^ (-4 * 12))
Simplifying the equation:
Monthly Payment = $15200 * 0.00567 / (1 - (1 + 0.00567) ^ (-48))
Using a calculator or spreadsheet software, we can evaluate the right side of the equation to find the final answer. The resulting value will be the monthly payment for the car loan.