You plan on saving $$100$ per month $($at the end of every month$)$ towards retirement, and you plan to retire in $45$ years. Assume the interest is $3\%$ compounded monthly, and that you currently don't have any funds in the retirement account.

a$.$ How much will you have in your retirement account when you retire?

i$.$ $$114,322\mathrm{.}39$

ii$.$ $$9,271\mathrm{.}99$

iii. $$54,000\mathrm{.}00$

iv$.$ $$114,037\mathrm{.}30$

b$.$ Things happened along the way, and you were able to save $$100$ per month the first $4$ years, then nothing for the next $15$ years, then $$200$ per month for the remainder of the months until retirement. How much will you have at retirement?

i$.$ $$99,441\mathrm{.}11$

ii$.$ $$29,017\mathrm{.}91$

iii. $$67,200\mathrm{.}00$

iv$.$ $$111,746\mathrm{.}00$