$1000 is invested at4.8% compounded continuously, how long will it take for the account to reach $2500?

• Standard formula for Compound Interest is FV = PV(1+i/n)^(n*t), where
  
  FV = future value of the money, $2,500
  PV = present value of the money, $1,000
  i = annual interest rate, 4.8%
  n = number of compounding periods per year, 1
  t = number of years
  therefore 2500 = 1500 (1+4.8/100)^t
  (2500/1500) = (1.048)^t
  2.5 = (1.048)^t
  Take natural log of both the sides..
  ln(2.5) = t * ln(1.048)
  when we have exponent inside log, you need to bring it out as coefficient
  therefore t = ln(2.5) /ln(1.048)
  Type it in Google search (it will show calculator) and final answer is
  19.54 years.
  
  You can validate this answer by using same formula for FV (Future Value)
  1000(1.048)^19.54 where 1000 is Present Value, 0.048 is 4.8% interest and t = time = 19.54 years. Enter this equation in google calculator and you will get FV = 2499.53638447 which equals to 2500.
• 10 years agoHelpfull: Yes(0) No(0)