Recall the formula for growth of a sum of money :
A = P (1 + r)^t
where
A = Value after t time periods
P = Principle (Starting value)
r = rate per time period t
t = number of time periods
For this problem,
P = 12000
r = .15
t = 3
First, we must solve for A. Then we will take A-P to determine the interest paid.
A = P ( 1 + r)^t
A = 12000 (1 + .15)^3
A = 12000 (1.15)^3
A = $18,250.50
Thus, the amount after 3 years is $18,250.50. Since the initial amount borrowed was $12,000, Jack has accrued
A - P = 18250.50 - 12000 = $6250.50
in interest.
