Fritz benjamin buys a car costing $8300. He agrees to make payment at the end of each month period for 8 years. He pays 7.2% interest compounded monthly. what is the amount of each payment? find the total amount of interest fritz will pay?
TVM Calculator
N=96
I=7.2
PV=8300
PMT=Alpha Enter
FV=0
P/Y=12
C/Y=12
END
Total Interest: Multiply 9 by the monthly payments
To find the amount of each payment, we can use the formula for calculating a loan payment, known as the monthly payment formula. The formula is given by:
P = (r(PV)) / (1 - (1 + r)^(-N))
Where:
P = Monthly payment
r = Monthly interest rate
PV = Present value or loan amount
N = Total number of payments
Using the given information:
PV = $8300
N = 8 years * 12 months/year = 96 months
r = 7.2% / 100 / 12 = 0.006
Substituting the values into the formula:
P = (0.006 * 8300) / (1 - (1 + 0.006)^(-96))
P ≈ $110.11
Therefore, the amount of each payment will be approximately $110.11.
To find the total amount of interest Fritz will pay, we can subtract the loan amount from the total payments made over 8 years.
Total Payments = Monthly Payment * Total number of payments
Total Payments = $110.11 * 96
Total Payments ≈ $10,577.76
Interest Paid = Total Payments - Loan Amount
Interest Paid ≈ $10,577.76 - $8300
Interest Paid ≈ $2277.76
Therefore, Fritz will pay approximately $2,277.76 in total interest.
To find the amount of each monthly payment, we can use the formula for calculating the fixed monthly payment of a loan:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
PV = Present value of the loan (car cost)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments
First, let's calculate the variables needed for the formula:
PV = $8300 (car cost)
r = 7.2% / 100 / 12 = 0.006
n = 8 years * 12 months/year = 96 months
Now, we can substitute these values into the formula:
P = (0.006 * 8300) / (1 - (1 + 0.006)^(-96))
P ≈ $114.43 (rounded to the nearest cent)
So, the amount of each monthly payment that Fritz needs to make is approximately $114.43.
To find the total amount of interest Fritz will pay over the 8-year period, we can subtract the initial car cost from the total amount paid over the loan period:
Total amount paid = Monthly payment * Total number of payments
Total amount paid = $114.43 * 96 = $10,999.28 (rounded to the nearest cent)
Total interest paid = Total amount paid - Car cost
Total interest paid = $10,999.28 - $8300 = $2699.28 (rounded to the nearest cent)
Therefore, Fritz will pay a total of approximately $2699.28 in interest over the 8-year period.
PV = 8300
payment --- p
i = .072/12 = .006
n= 8(12) = 96
p(1 - 1.006^-96)/.006 = 8300
solve for p
Wow, 8 years to pay off a car ?