Question

Which recursive definition models the growth of a one time investment of $6000 in a bank account with a yearly interest of 3% compounded monthly after n years

Answer 1

First, we determine the effective interest rate given that the money is compounded monthly at 3%. That is,
ieff = (1 + i/12)^12 - 1
Substituting,
ieff = (1 + 0.03/12)^12 - 1 = 0.0304
The model to describe the growth of money after n years is therefore expressed as,
F = ($6000) x (1 + 0.0304)^n