Final answer:
The principal repayment in the 6th payment is calculated by finding the interest portion of the payment based on the remaining loan balance and the 5.2% interest rate, and then subtracting this from the total payment amount of $1200..
Step-by-step explanation:
To calculate the principal repayment in the 6th payment of a loan with a 5.2% effective annual interest rate, we will first find the interest portion of the 6th payment. Assuming the payments are made at the end of each year and the interest is compounding annually, the remaining loan balance right before the 6th payment can be calculated. After the 5th payment of $1200, the loan will have compounded interest for 5 years on the initial amount, minus the interest and principal paid in each of the previous payments.
The interest portion of the 6th payment is the product of the remaining balance and the interest rate. Subtracting this interest portion from the total payment of $1200 gives us the principal repayment amount. As we need two lines for our final answer and a detailed but concise explanation in 120 words as well as a further expanded explanation in 250 words, the precise mathematical operations involve calculating compound interest on the diminishing balance and subtracting the interest portions from the payments accrued up to the 6th payment.