Final answer:
The average annual compound rate of interest on Sarah’s loan is approximately a. -6.89%, which indicates a negative interest rate where the amount owed decreases over time. This is calculated using the compound interest formula by equating the amount paid back after 5 years to the formula that includes the principal and interest rate.
Step-by-step explanation:
The average annual compound rate of interest on Sarah’s loan from her aunt can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the amount after time t, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In Sarah's case, she borrowed $10,000 and paid back $7,000 after 5 years. Assuming the interest was compounded annually (n=1), we can equate her payback to the formula:
$7,000 = $10,000(1 + r)^5
By solving this equation, we can calculate r to find the average annual compound rate of interest. After calculating, we find that the annual compound rate is approximately -6.89%, which means Sarah's aunt charged a negative interest rate, implying that the amount owed decreased over time without any payments being made.
Therefore, the correct answer is:
a. -6.89%