Victor would like to buy his first car and the one he has his eye on is $25,000 plus an extra 13% HST for a total price of $28,250. The dealership has a deal for 0% down payment and charges 2.89% interest on the loan. Victor plans to make car loan payments weekly and has accepted the maximum loan repayment period of 8 years.
How much will his weekly care loan payment be?
To make the standard formula to work, the interest rate must be compounded weekly
i = .0289/52 = .000555769 , I will store that in my calculator's memory for best accuracy.
n = 52*8 = 416 weeks
payment --- p
p(1 - 1.00555...^-416)/.00055.. = 28250
solve for p
Hint, you should get a bit over $75
let me know what you got
I got around $76.08
There's a follow up question for this word problem and it's
How much will he have paid to the dealership by the time his loan is paid off?
I answered that question by multiplying $76.08 how many weeks are in a month and multiplied it by 12 and multiply by 8 again but I'm not sure if I did this correctly
The $76.08 is correct
But you should have multiplied it by 416 in one step
When you multiply the number of weeks in a month, usually 4, then by 12 and 8
you don't get 416
4x12 = 48, but there are 52 weeks in a year
so you need 52x8 = 416
To calculate Victor's weekly car loan payment, we need to follow a few steps:
Step 1: Calculate the loan amount
Since Victor is not making any down payment, the loan amount will be equal to the total price of the car, which is $28,250.
Step 2: Calculate the interest rate per week
The yearly interest rate is given as 2.89%. To calculate the interest rate per week, divide it by the number of weeks in a year. Since Victor plans to make weekly payments, the number of weeks in a year is 52.
So, the interest rate per week is (2.89 / 100) / 52 = 0.005519 = 0.55%
Step 3: Calculate the number of payments
Victor plans to repay the loan over 8 years, and since he wants to make weekly payments, we need to calculate the total number of weeks. To get the total number of weeks, multiply the number of years by 52 (weeks in a year).
Total number of weeks = 8 years * 52 weeks/year = 416 weeks
Step 4: Calculate the weekly car loan payment
To calculate the weekly car loan payment, we can use the loan amortization formula:
P = (r * A) / (0.01 - (1 + r)^(-n))
Where:
P = Payment amount (weekly car loan payment)
A = Loan amount ($28,250)
r = Interest rate per week (0.55% or 0.0055 as a decimal)
n = Total number of payments (416 weeks)
Plugging in the values:
P = (0.0055 * 28250) / (0.01 - (1+0.0055)^(-416))
Using this formula, we calculate that Victor's weekly car loan payment will be approximately $70.72.