A sum of money is invested at 12 percent compounded quarterly. About how long will it take for the amount of money to double? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years
For the amount to double, set the growth factor equal to 2: 2 = (1 + 0.12/4)^(4t) = 1.03^(4t). Taking natural logarithms gives t = ln(2)/(4 ln(1.03)) ≈ 5.86 years, which rounds to 5.9 years. Therefore, the correct choice is 5.9 years.
AI-written and checked against the verified answer.