Nov 15, 2011 #1 E Enlong New member Joined Nov 15, 2011 Messages 0 Reaction score 0 Points 0 How long will it take an investment to quadruple in an an account that earns 5% interest rate compounded continuously?
How long will it take an investment to quadruple in an an account that earns 5% interest rate compounded continuously?
Nov 17, 2011 #2 M MagicMatt New member Joined Jul 29, 2008 Messages 6 Reaction score 0 Points 1 The formula for continuously compounded interest is A = Pe^(rt) where: A = final amount, after 't' years P = principal (starting) amount r = interest rate t = time, in years So plug in some numbers. Let's say you start with $1,000, and you want to quadruple that into $4,000. 4000 = 1000e^(0.05t) Now solve for t: 4 = e^(0.05t) ln(4) = ln(e^(0.05t)) ln(4) = 0.05t ln(4)/0.05 = t 27.725 = t So, it would take almost 27 years and 9 months.
The formula for continuously compounded interest is A = Pe^(rt) where: A = final amount, after 't' years P = principal (starting) amount r = interest rate t = time, in years So plug in some numbers. Let's say you start with $1,000, and you want to quadruple that into $4,000. 4000 = 1000e^(0.05t) Now solve for t: 4 = e^(0.05t) ln(4) = ln(e^(0.05t)) ln(4) = 0.05t ln(4)/0.05 = t 27.725 = t So, it would take almost 27 years and 9 months.
Nov 17, 2011 #3 V Victor Member Joined May 16, 2008 Messages 298 Reaction score 0 Points 16 The future value of an initial principal amount compounded continuously is given by this: FV = P(e^rt) where e is the exponential constant 2.718... etc, r is the rate of growth and t is the number of periods. In this case, we want FV = 4P So we are looking for 4P = P(e^0.05t) since the interest rate is 5 per cent. So e^0.05t = 4 by dividing both sides by P So 0.05t = ln(4) using natural logs So t = ln(4)/0.05 = 1.3863/0.05 = 27.726 periods. OK?
The future value of an initial principal amount compounded continuously is given by this: FV = P(e^rt) where e is the exponential constant 2.718... etc, r is the rate of growth and t is the number of periods. In this case, we want FV = 4P So we are looking for 4P = P(e^0.05t) since the interest rate is 5 per cent. So e^0.05t = 4 by dividing both sides by P So 0.05t = ln(4) using natural logs So t = ln(4)/0.05 = 1.3863/0.05 = 27.726 periods. OK?