How long does it take or an investment to double in value if

How long does it take (or an investment to double in value if it is invested at 3% compounded quarterly? Compounded continuously? At 3% compounded quarterly, the investment doubles in about years. (Round to two decimal places as needed.)

Solution

let investment = $ x

amount = 2x

rate of interest = 3% compounded quarterly

hence, applying the formula

A = P ( 1+ r/4 ) ^4t

2x = x ( 1 + .03/4 ) ^ 4t

2 = ( 1.0075)^4t

taking ln on both sides

ln 2 = 4t ln (1.0075 )

4t = 92.7657

t = 92.7657 / 4 = 23.20

investement doubles in 23.2 years