Your purchase cost $5200 including tax. You sign an installment loan for $2200 after the down payment. The remainder including the finance charge will be paid in 22 equal monthly installments of $114.66 at 16% interest. What is the amount of interest paid each month?
This is a nonsensical over-simplification of the problem by the bot
In any type of installment plan in 2023, compound interest would be used.
The monthly payment would be the sum of the interest plus the actual repayment of the loan. At the beginning of the term the interest would be a major part, and it would decrease as the term progresses.
Also the bot misread the first part of the question.
It said: You sign an installment loan for $2200 after the down payment. The bot continued as if the downpayment was 2200. The actual loan is 3000,
not 2200
I apologize for the errors in my previous response. As an AI language model, I aim to provide helpful responses to the best of my abilities. However, I am not perfect and there may be times when I make mistakes or oversimplify problems. Thank you for bringing this to my attention.
btw, ....
i = .16/12 = .01333...
n = 22
paym = ? (it said it was 114.66)
PV = 2200
2200 = paym( 1 - 1.013333...^-22)/0.013333....
paym = 116.04
So there is a contradiction in the original problem
Thank you for pointing out this contradiction. It appears that there may be an error in the original problem, as the calculated monthly payment does not match the given monthly payment of $114.66. As an AI language model, I am not able to verify the accuracy of the original problem, but I apologize for any confusion my previous response may have caused.
To determine the amount of interest paid each month on an installment loan, we first need to calculate the total interest paid over the entire loan period.
First, let's calculate the total loan amount by subtracting the down payment from the purchase cost:
Total loan amount = Purchase cost - Down payment
Total loan amount = $5200 - $2200 = $3000
Next, we calculate the total interest paid over the loan period:
Total interest = Total loan amount × Interest rate
Total interest = $3000 × 16% = $480
Now, let's calculate the monthly interest paid. Since the interest is distributed evenly over 22 months, we divide the total interest by the number of installments:
Monthly interest = Total interest / Number of installments
Monthly interest = $480 / 22 ≈ $21.82
Therefore, the amount of interest paid each month on this loan is approximately $21.82.
First, we need to calculate the total amount that will be paid for the loan:
Total loan amount = Loan amount + Finance charge
Total loan amount = $5200 - $2200
Total loan amount = $3000
Finance charge = Total loan amount x Interest rate x Loan term
Loan term = 22 months
Finance charge = $3000 x 16% x (22/12)
Finance charge = $880
Total amount to be paid = Loan amount + Finance charge
Total amount to be paid = $2200 + $880
Total amount to be paid = $3080
Now, we can calculate the amount of interest paid each month:
Interest per month = Total finance charge / Loan term
Interest per month = $880 / 22
Interest per month = $40
Therefore, the amount of interest paid each month is $40.