Answer:
The interest for the first payment is $8.31 and the payment to principal is $245.69
Explanation:
We can use the loan formula to calculate the interest and payment to principal for the first payment. The loan formula is:
P = (r * A) / (1 - (1 + r)^(-n))
where P is the monthly payment, A is the loan amount, r is the monthly interest rate, and n is the total number of payments.
To find the interest and payment to principal for the first payment, we can first calculate the loan amount, which is the present value of the loan:
A = P * ((1 - (1 + r)^(-n)) / r)
where P is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
In this case, P = $254.00, r = 0.1/12 (since the annual interest rate is 10% and there are 12 months in a year), n = 48, so we have:
A = $254.00 * ((1 - (1 + 0.1/12)^(-48)) / (0.1/12)) = $9,976.28
This means that Candy borrowed $9,976.28 to add the additional room to her home.
To calculate the interest and payment to principal for the first payment, we can use the following formulas:
Interest = r * A
Payment to Principal = P - Interest
Plugging in the values, we get:
Interest = (0.1/12) * $9,976.28 = $8.31 (rounded to the nearest cent)
Payment to Principal = $254.00 - $8.31 = $245.69 (rounded to the nearest cent)
Therefore, the interest for the first payment is $8.31 and the payment to principal is $245.69.