Final answer:
To find the future value A of a loan with principal P of $4000 at a simple interest rate of 6.5% for 4 months, first calculate the interest ($86.67), then add it to the principal to get the future value, which is $4086.67.
Step-by-step explanation:
To calculate the future value A, or the total amount due at time t, with the principal P borrowed at a simple interest rate r for a period of time, we can use the formula:
Future Value (A) = Principal + (Principal × rate × time)
In this case, the Principal (P) is $4000, the annual interest rate (r) is 6.5%, and the time (t) is 4 months, which we need to convert into years to match the annual rate. Since there are 12 months in a year, 4 months is ⅓ year (or 4/12).
Interest = Principal × rate × time
Interest = $4000 × 0.065 × (4/12)
Interest = $4000 × 0.065 × 0.333...
Interest = $86.67 (approximately)
Now, we add the interest to the principal to find the future value (A).
A = Principal + Interest
A = $4000 + $86.67
A = $4086.67
Thus, the loan's future value A, or the total amount due at the end of 4 months, is $4086.67.