Carmen needs $3560 for future project. She can invest $2000 now at annual rate of 7.8%, compound monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

  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.

irrational, cannot