How long does it take for an investment to double in value i

How long does it take for an investment to double in value if it is invested at 5% compounded quarterly? Compounded continuously? At 5% compounded quarterly, the investment doubles in about years. (Round to two decimal places as needed.)

Solution

A=P(1+r/n)^(n*t)

Let P=x

therefore A=2x

and compounded quarterly therefore n=4 here

2x=x(1+.05/4)^(4t)

2= 1.0125^(4t)

taking log on both sides

log2/log1.o125=4t

t=1/4(log2/log1.0125)

t=13.95 yrs

Compounded continuously

A=Pe^(rt)

2x=1x * e^(.05 t)

2=e^(.05t)

taking ln on both sides

ln 2/.05=t

t=13.86