Final answer:
To determine the interest portion of Sylvain's first loan payment, the monthly interest rate of 0.61583% is applied to the loan amount, resulting in $1,231.66 going towards interest. Calculating the principal portion would require knowing the total monthly payment, which is not provided.
Step-by-step explanation:
To figure out how much of the first payment on Sylvain's loan will go toward interest, and how much will go toward the principal, we need to understand how loans are amortized. Loans are typically paid back with monthly payments that include both interest and principal repayment components. The interest for each payment is calculated based on the remaining balance of the loan.
First, we calculate the monthly interest rate by dividing the annual rate by 12. In this case, the monthly interest rate is 7.39% divided by 12, which equals 0.61583% (or 0.0061583 in decimal form). The initial interest payment is then calculated by multiplying the initial loan amount by the monthly interest rate.
Interest portion of the first payment is: $200,000 * 0.0061583 = $1,231.66
The actual monthly payment amount isn't given, but it would typically be calculated using an amortization formula that takes into account the principal, the interest rate, and the number of payments over the life of the loan. To find out how much of the first payment goes to the principal, you'd subtract the interest portion from the total monthly payment. Without the actual monthly payment amount, we can't provide the principal portion.