Final answer:
The future value A of the loan after 9 months at a simple interest rate of 3.5% on a principal of $4000 is $4105.
Step-by-step explanation:
To find the loan's future value A, or the total amount due at the end of the period, we use the formula for simple interest: A = P + (P × r × t), where P is the principal, r is the annual interest rate, and t is the time in years. For the given values of P = $4000, r = 3.5% (or 0.035 when converted to decimal), and t = 9/12 year (since 9 months is three-quarters of a year), we calculate: A = $4000 + ($4000 × 0.035 × 9/12). By computing this, we get: A = $4000 + $105, which equals $4105.