Final answer:
Using the compound interest formula, it would take approximately 33.1 years for an investment of $32,000 at an annual interest rate of 2.16% compounded monthly, to double.
Step-by-step explanation:
To determine how long it will take to double an investment of $32,000 at 2.16% interest compounded monthly, we utilize the formula for compound interest, which is A = P(1 + r/n)^(nt). Where A is the amount of money accumulated after n years, including interest, P is the principal amount ($32,000), r is the annual interest rate (0.0216), n is the number of times that interest is compounded per year (12), and t is the time the money is invested or borrowed for, in years. Since we want to double our money, A will be $64,000. By rearranging the formula to solve for t, we have t = (log(A/P)) / (n · log(1 + r/n)).
Substituting the numbers we get t = (log(64000/32000))/(12 · log(1 + 0.0216/12)). Using a calculator, t equals approximately 33.1 years.
It will take about 33.1 years for the investment to double.