You have arranged for a loan on your new car that will require the first payment today. The loan is for $32,000, and the monthly payments are $620.
Required:
If the loan will be paid off over the next 60 months, what is the APR of the loan?
32000 = 620 + 620( 1 - (1+i)^-59)/i
My favourite webpage, Wolfram, says
http://www.wolframalpha.com/input/?i=32000+%3D+620+%2B+620%28+1+-+%281%2Bx%29%5E-59%29%2Fx
i = .0052576 or
12i = .06309
which is 6.309% per annum , compounded monthly
(look past all that messy output to where it says,
real solution x = .0052576
Why did the car need a loan? Because it couldn't make enough dough on its own! But let's crunch some numbers, shall we?
To figure out the APR of the loan, we need to calculate the total amount paid over the 60-month period.
Total amount paid = Monthly payment * Number of months
Total amount paid = $620 * 60 = $37,200
Now, let's find out the total interest paid by deducting the loan amount from the total amount paid.
Total interest paid = Total amount paid - Loan amount
Total interest paid = $37,200 - $32,000 = $5,200
Next, let's determine the APR (Annual Percentage Rate). To do that, we'll divide the total interest paid by the loan amount and multiply it by 100.
APR = (Total interest paid / Loan amount) * 100
APR = ($5,200 / $32,000) * 100
Grab your calculator (or just trust me on this one) and you'll find that the APR of the loan is approximately 16.25%.
So, remember, the car may have needed a loan, but at least it rode off with a pretty decent APR!
To calculate the APR (annual percentage rate) of the loan, we need to know a few additional details. Specifically, we need to know the total amount paid over the loan term (60 months) and the interest paid on the loan. With this information, we can calculate the APR using the following steps:
Step 1: Calculate the total amount paid over the loan term:
Total amount paid = Monthly payment * Number of months
Total amount paid = $620 * 60
Total amount paid = $37,200
Step 2: Calculate the interest paid on the loan:
Interest paid = Total amount paid - Loan amount
Interest paid = $37,200 - $32,000
Interest paid = $5,200
Step 3: Calculate the APR using the formula:
APR = (Interest paid / Loan amount) * (12 / Number of months) * 100
APR = ($5,200 / $32,000) * (12 / 60) * 100
APR = (0.1625) * (0.2) * 100
APR = 3.25
Therefore, the APR of the loan is 3.25%.
To calculate the APR (Annual Percentage Rate) of a loan, you need to gather some information and use a formula. The APR represents the total cost of borrowing, including both the interest rate and any additional fees or charges associated with the loan.
In this case, you have the loan amount, the monthly payment, and the loan term. Here's how you can proceed to calculate the APR:
1. Calculate the total amount paid over the loan term: Multiply the monthly payment by the number of months. In this case, the monthly payment is $620, and the loan term is 60 months. So, the total amount paid would be 620 x 60 = $37,200.
2. Calculate the total interest paid: Subtract the loan amount from the total amount paid. In this case, the loan amount is $32,000. So, the total interest paid would be $37,200 - $32,000 = $5,200.
3. Calculate the APR: Divide the total interest paid by the loan amount, then divide the result by the loan term in years (assuming the loan term is in months). Finally, multiply the result by 100 to express it as a percentage.
APR = (Total Interest Paid / Loan Amount) / (Loan Term in Years) * 100
In this case, the total interest paid is $5,200, the loan amount is $32,000, and the loan term is 60 months (which is equal to 5 years). So, the APR calculation would be:
APR = ($5,200 / $32,000) / 5 * 100 = 0.0325 * 100 ≈ 3.25%
Therefore, the APR of the loan is approximately 3.25%.