How long in years and months will it take for an investment

How long (in years and months) will it take for an investment to double at 3% compounded monthly? (please show work)

Solution

The formula for compound interest is F = P[ 1+ (r/n)]^nt where P is the principal/initial amount, n is the number of periods per year, t is the number of years and r is the rate of interest in decimals per period. Here, F = 2P, r = 3%/12 = 3/1200 = 0.0025 and n = 12. We have to find t. Then 2P = P[1 +(.0025)]^12t or, (1.0025)^12t= 2 On  taking logarithm of both sides, we get 12t log 1.0025 = log 2 or 12t * 0.001084381292 = 0.301029995. Then t = 0.301029995/ (12*0.001084381292) = 23.13377514 years = (23.13377514)*12 months = 277.605 months = 278 months ( approximately, on rounding off to the nearest whole number)