Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily, and continuously.

Question

Answer 1

2 = (1.1)^t

log_1.12 = t = doubling time at 10% interest rate

t = ln2/ln1.1 = about 7.27 years compounded annually

for monthly

2 =(1+ .1/12)^12t

solve for t

for daily compounding

2 = (1+.1/365.25)^365.25t

solve for t

for continuous compounding

2 = e^.1t

ln2 = .1t

t = ln2/.1 = 10ln2 = about 6.93 years

general formula for doubling time is

2 =(1+r/n)^nt where n= number of compounding periods per year, r= interest rate, t=years

or for continuous compounding where n approaches infinity, the above formula reduces to

2= e^rt where r= interest rate, t=years and e = an irrational number about 2.718281828...