Sam purchased a used car for $14,750. He put $2,000 down and financed the rest with a 48-month, 7.5% loan.
What is his monthly car payment? Round your answer to the nearest cent.
P ( r / 12 )
-------------------------
-m
(1 - ( 1 + r / 12 ) )
represented by this equation
15000 ( 0.07/ 12 )
-------------------------
-36
(1 - ( 1 + 0.07 / 12 ) )
solving this would give
92.1875
------
0.25849
= a payment of $356.64 each month for 48 months
-m and -36 are exponents of the bottom equation and i meant to but -48 not -36 in the equation a typo my bad
( 1 + 0.07 / 12)^(-48)
To find Sam's monthly car payment, we need to consider the amount financed and the terms of the loan.
The amount financed is the total cost of the car minus the down payment. In this case, the total cost of the car is $14,750, and Sam put down $2,000, so the amount financed is $14,750 - $2,000 = $12,750.
Now, let's calculate the monthly payment using the amount financed, the loan term (48 months), and the interest rate (7.5%).
To calculate the monthly payment, we can use the formula for an amortizing loan:
Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Principal loan amount (amount financed)
r = Monthly interest rate (Annual interest rate / 12)
n = Total number of payments (loan term)
Let's plug in the values:
P = $12,750
r = 7.5% / 12 = 0.00625 (monthly interest rate)
n = 48
Now, let's calculate the monthly payment using the formula:
Monthly payment = $12,750 * (0.00625 * (1 + 0.00625)^48) / ((1 + 0.00625)^48 - 1)
After performing the calculations, the monthly car payment for Sam's loan is approximately $300.91 (rounded to the nearest cent).
Therefore, Sam's monthly car payment is $300.91.