Charlie changed car insurance companies and received an insurance policy covering two vehicles for $6$ months for a premium of $$650$ plus $$32\mathrm{.}50$ sales tax. The new policy takes effect on Dec. $1.$ Charlie was given three options to pay this amount. The first option was to pay the $$682\mathrm{.}50$ on Dec. $1.$ The other two options consisted of paying the premium in instalments as follows:

$($a$)$ Option $2$ allows Charlie to pay the premium over the next $6$ months. The insurance company levels a financing charge of $3\%$ on the premium $($not including the tax$).$The total premium $($$$650,$ plus $$19\mathrm{.}50$ finance charge, plus $$32\mathrm{.}50$ tax $=$ $$702)$ is then divided by $6$ to get a monthly payment of $$117.$ However, the company requires the first two months$$ payments up front $($i$.$e$.$ on Dec. $1),$ with the four remaining payments made at start of each of the next four months. The insurance company claims it is charging Charlie an annual rate of interest of only $3\%.$ What is the actual EAR?

$($b$)$ An insurance broker provides a third option, which he claims avoids a $3\%$ financing charge. For a $$15$ service fee, Charlie can pay the premium in $3$ equal monthly instalments, with the first payment paid on Dec. $1.$ The monthly payment would be $$232\mathrm{.}50($i$.$e$.$ $$650$ plus $$32\mathrm{.}50$ tax plus $$15$ service fee all divided by $3).$ Is this a better deal?