Question $4.(20$pts$)$

Crse Study: Car Insurance Premiums

Charlie changed car insurance oompanies and received an insurance policy covering two velicles for $6$ wouths for a preminm of $$650$ plus $$32\mathrm{.}50$ sales tax. The new policy talos eflect on Deec $1.$ Charlie was geven three options to pay this amount. The first option was to pry the $$6\mathrm{.}2\mathrm{.}50on$ Dec. $1.$ The other two options consisted of paying the pecmium is instalments nos follows.

$($a$)$ Oetion $2$ allows Charlie to pav the paet wume the foxt $6$ moths. The insurance cotupany levils a financing charge of Jhi on the premium $($not inclading the tax$).$ The total peemium $(6S9,$ plas $$19\mathrm{.}50$ finasce charge, plus $$32\mathrm{.}50$tax$=$$$702)$ is then divishd by $6$ to get is monlly payment of $$117.$ However, the company remaining poymets made at start of each of the mext four months. The insurance compary claims in is charging Clartic an ansual rate of interest of only $3\%.$ What

is ahe actal FAR? is the actas! EAR?

$(1)$ An inemance holes peovids athird optisa, which he claims avoids a $3\%$ finaticing charg., Foe a $$15$ mrvice fox, Chatlie can pay the pevmium is $3$ equal moathly inotaluzeAk, with the fint paymerst pasid on Dee. $1.$ The monthly payment would is better dral?