Shelia bought a new computer for 2000 dollars and has agreed to finance it at 12% interest, with 100 dollar payments each month. When she makes her first payment next month, how much will she pay for interest alone?
I will assume the interest rate is 12% per annum, compounded monthly, so the montyly rate is 1%
interest in the first month = 2000(.01) = $20
To determine how much Sheila will pay for interest alone on her new computer, we need to follow these steps:
Step 1: Calculate the total interest paid over the course of the financing period.
First, we calculate the total interest paid over the course of the financing period using the formula:
Total Interest = Total Amount Paid - Principal Amount
The principal amount is the price of the computer, which is $2000.
The total amount paid can be calculated using the formula:
Total Amount Paid = Monthly Payment * Number of Payments
Since the monthly payment is $100, and Sheila will be making these payments each month, the number of payments will be the same as the number of months.
Step 2: Calculate the number of payments.
Since Sheila is making monthly payments, and she will make her first payment next month, we can calculate the number of payments by subtracting the current month from the last month.
For example, if it is January now and her final payment will be in December, then the number of payments will be (12 - 1) = 11.
Step 3: Calculate the total amount paid.
Total Amount Paid = Monthly Payment * Number of Payments
Total Amount Paid = $100 * 11 = $1100
Step 4: Calculate the total interest paid.
Total Interest = Total Amount Paid - Principal Amount
Total Interest = $1100 - $2000 = -$900
Since the total interest is negative, it means that the interest alone is $0. This occurs when the monthly payments are larger than the interest, effectively causing Sheila to pay off the computer before the interest has accrued. Therefore, in this scenario, Sheila will not pay any interest alone when she makes her first payment next month.