Your purchase costs, $4, 400, including tax. You sign an installment loan for $2, 500 after the down payment. The remainder including the finance charge will be paid in 20 equal monthly installments of $126.17 at 18% interest. What is the new balance after one month?
To find the new balance after one month, we need to first calculate the finance charge for one month:
18% annual interest rate = 1.5% monthly interest rate
Finance charge for one month = 1.5% of $2,500 = $37.50
Next, we need to subtract the monthly payment from the previous balance (which includes the finance charge):
$126.17 - $37.50 = $88.67
Finally, we subtract the monthly payment from the previous balance:
$2,500 + $37.50 - $126.17 = $2,411.33
Therefore, the new balance after one month is $2,411.33.
This is a very easy question, since it wants the balance after only the first
month.
interest for 1st month = .015(2500) = $37.50
so the repayment = $126.17- $37.50 = 88.67
Balance after 1 month = 2500 - 88.67 = $$2411.33
A much more interesting question would have been:
What is the balance after 10 months.
btw, the payment of $126.17, as stated in the question, is incorrect
Should have been:
2500 = paym( 1 - 1.015^-20)/.015
paym = $145.61
Thank you for pointing out the error in the payment amount, and for providing a more interesting question! Here's the calculation for the balance after 10 months:
First, we'll calculate the correct monthly payment amount:
2500 = paym(1 - 1.015^-20)/0.015
paym = $145.61
Next, we'll calculate the balance after 10 months:
n = 10 (number of months)
r = 1.5% (monthly interest rate)
P = 2500 (loan amount)
balance after 10 months = P(1 + r)^n - (paym/r)((1 + r)^n - 1)
balance after 10 months = 2500(1 + 0.015)^10 - (145.61/0.015)((1 + 0.015)^10 - 1)
balance after 10 months = $1,468.49
Therefore, the balance after 10 months is $1,468.49.
To calculate the new balance after one month, we need to understand the breakdown of the installment loan and the finance charge.
Given information:
- Total purchase cost (including tax): $4,400
- Down payment: $2,500
- Loan amount: $4,400 - $2,500 = $1,900
- Number of installments: 20
- Monthly installment amount: $126.17
- Interest rate: 18% per year
To calculate the finance charge for one month, we can use the formula:
Finance Charge = (Loan Amount * Interest Rate * Time) / 12
Given that the time is one month (1/12 of a year), we can substitute the values into the formula:
Finance Charge = ($1,900 * 0.18 * (1/12)) / 1
Please note that the finance charge needs to be added to the loan amount to determine the new balance.
Calculating the finance charge:
Finance Charge = ($1,900 * 0.18 * (1/12)) / 1
= $2.85
Adding the finance charge to the loan amount, we get:
New Balance = Loan Amount + Finance Charge
= $1,900 + $2.85
= $1,902.85
Therefore, the new balance after one month would be $1,902.85.