A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double? compound interest formula:mc009-1. Jpg t = years since initial deposit n = number of times compounded per year r = annual interest rate (as a decimal) p = initial (principal) investment v(t) = value of investment after t years 5. 9 years 6. 1 years 23. 4 years 24. 5 years.