The price of a new car is $16,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent.)
What monthly payment will she be required to make if the car is financed over a period of 48 mo? Over a period of 72 mo?
What will the interest charges be if she elects the 48-mo plan? The 72-mo plan?
$12,000 loan amount
r = .06/12 = .005
n = 48 or 72
1+r = 1.005
(1+r)^-n = .7871 for n = 48
1 - (1+r)^-n = .2129 for n = 48
payment = loan [ r/(1 -(1+r)^-n ) ]
payment for 48 months = 12,000[.005/.2129]
=$281.82
now you do the 72 months
i got $198.87
what about the interest charges?
LOL
well
12,000/48 = 250 per month with no interest.
you paid 281.82 including the interest at 6% compounded monthly
(281.82-250)*48?
right
Determine the simple interest rate at which will grow to in the months. Round your answer to the nearest tenth of percent
To calculate the monthly payment for a car loan, you can use the formula for calculating the monthly payment of a loan. The formula is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Loan amount (total price of the car minus down payment)
r = Monthly interest rate (annual interest rate divided by 12 and then divided by 100)
n = Number of monthly payments (loan term in months)
Let's calculate the monthly payment for the 48-month plan:
1. Calculate the loan amount (P): P = Price of the car - Down payment
P = $16,000 - (25% * $16,000)
P = $16,000 - $4,000
P = $12,000
2. Calculate the monthly interest rate (r): r = 6% / 12 / 100
r = 0.06 / 12
r = 0.005
3. Calculate the number of monthly payments (n): n = 48
4. Plug the values into the formula and calculate the monthly payment (M):
M = $12,000 * (0.005 * (1 + 0.005)^48) / ((1 + 0.005)^48 - 1)
Calculating this value will give you the monthly payment for the 48-month plan.
Repeat the steps using n = 72 to calculate the monthly payment for the 72-month plan.
To calculate the interest charges for each plan, you can multiply the monthly payment by the number of payments and subtract the total loan amount:
Interest Charges = (Monthly Payment * Number of Payments) - Loan Amount
Again, repeat the steps for both plans to calculate the respective interest charges.