Charlie changed car insurance companies and received an insurance policy covering two vehicles for 6 months for a premium of $650 plus $32.50 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 $682.50 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 $19.50 finance charge, plus $32.50 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 $232.50 (i.e. $650 plus $32.50 tax plus $15 service fee all divided by 3). Is this a better deal?

Please answer a) and b). Thank you :)