Answer:
7.42 years (7 years 5 months)
Step-by-step explanation:
The future value of Carmen's account can be modeled by
FV = P(1 +r/12)^(12t)
where P is the principal invested, r is the annual rate, and t is the number of years.
Solving for t, we have ...
FV/P = (1 +r/12)^(12t)
log(FV/P) = 12t·log(1 +r/12)
t = log(FV/P)/(12·log(1 +r/12))
For FV = 3560, P=2000, r = 0.078, the time required is ...
t = log(3560/2000)/(12·log(1 +.078/12))
t ≈ 7.42
It will take Carmen about 7 years 5 months to reach her savings goal.
