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.
The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
