Final answer:
The principal amount of the loan is calculated using the formula: Principal = Interest / (rate × time). With an annual interest of $7,800 and an interest rate of 11%, the principal comes out to be $70,909.09.
Step-by-step explanation:
To find the principal amount of a loan when you know the total annual interest and the interest rate, you can use the formula Interest = Principal × rate × time. Since we know the annual interest ($7,800) and the interest rate (11%), and assuming the time applied here is 1 year, we can rearrange the formula to solve for the principal. This gives us Principal = Interest / (rate × time).
Let's plug in the numbers:
Principal = $7,800 / (0.11 × 1)
Principal = $7,800 / 0.11
Principal = $70,909.09
Therefore, the principal amount of the loan is $70,909.09, which corresponds to option a).