Question

You decide to put $175 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 3% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?

Answer 1

The future value (A) of a principal amount P compounded 12 times per year at rate r for t years is given by
  A = P·(1 + r/12)^(12t)

Substitute the given values and solve for t.
  3000 = 175·(1 + .03/12)^(12t)
Taking logarithms, this becomes
  log(3000) = log(175) + 12t·log(1.0025)
  (log(3000) -log(175))/(12·log(1.0025)) = t
  t ≈ 94.84

It will take 95 years for the balance to grow by a factor of 17 to $3000.