Mr. Steiner purchased a car for $14,000. Assuming his loan was compounded annually at an interest rate of 4.9% for 72 months.
Part A) How much will he pay in total for his new car?
Part B) How much did he pay in interest?
Part A) To calculate the total amount Mr. Steiner will pay for his car, we need to consider the total cost of the car including interest.
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount
P = principal amount (initial amount borrowed) = $14,000
r = annual interest rate = 4.9% or 0.049
n = number of times the interest is compounded per year = 1 (annual)
t = number of years = 72 months / 12 months/year = 6 years
Plugging in the values:
A = $14,000(1 + 0.049/1)^(1*6)
A = $14,000(1.049)^6
A = $14,000(1.315141)
A = $18,512.98
Therefore, Mr. Steiner will pay a total of $18,512.98 for his new car.
Part B) To calculate the amount paid in interest, we subtract the principal amount from the total amount:
Interest = Total amount - Principal amount
Interest = $18,512.98 - $14,000
Interest = $4,512.98
Therefore, Mr. Steiner paid $4,512.98 in interest for his new car.