Interest problems

Question

If you invested $1500 into an account with continuous compounding at a rate of 12.5%, how long will it take for your money to double?

Answer 1

The formula for continuously compounded interest is:

 

A = pe^rt

A = future amount = 2(1500) = 3000

p = principle investment = 1500

r = interest rate as a decimal = .125

t = time in years = unknown

 

We want the final total to be twice the principle investment so:

 

3000 = 1500e^.125t

Divide both sides by 1500

2 = e^.125t

Take the natural log of both sides

 

ln(2) = ln(e^.125t)

ln(2) = t*ln(e^.125)

ln(2) = .125t

 

t = ln(2)/.125

t = 5.545

 

Rounding this, it will take 5 1/2 yrs