The first step to determining the answer to this item is to calculate for the effective interest using the equation,
ieff = (1 + i/m)^m - 1 where ieff is the effective interest, i is the given interest and m is the number of compounding period.
Part A: m in this item is equal to 12. Substituting, ieff = (1 + 0.10/12)^12 - 1 = 0.1047
The amount of money after n years is calculated through the equation, An = A(1 + ieff)^n If An/A = 2 then, 2 = (1 + 0.1047)^n The value of n is 6.96 years
Part B: For the continuously compounding, An = Ae^(rt) An/A = 2 = e^(0.10t) The value of t is equal to 6.93 years.
