CAR INSURANCE PREMIUMS Charlie changed car insurance companies and received an insurance policy covering two vehicles for

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CAR INSURANCE PREMIUMS

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 (total $682.50). The new policy takes effect on 1 December. Charlie was given three options in which to pay this amount. The first option was to simply pay the $682.50 on 1 December 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 2 months' payments up front (i.e. on 1 December), with the 4 remaining payments made at the start of each of the next 4 months (1 Jan., 1 Feb., 1 March, 1 April). The insurance company claims it is charging Charlie an annual rate of interest of only 3%. (Better than you could get at a bank!) However, what is the actual rate, ji, being charged? (Use interpolation to calculate ) 1z and then calculate equivalent).)

b) Charlie is buying the insurance through a broker and the broker provides a third option, which he claims avoids the 3% financing charge. For a $15 service fee, Charlie can pay the premium in 3 equal, monthly instalments, with the 1st payment paid on 1 December. The monthly payment would be $232.50 (i.e. $650 plus $32.50 tax plus $15 service fee, all divided by 3). Is this really a better deal? To determine, calculate the actual rate, j1, being charged. (Again, use interpolation to calculate 112 and then calculate equivalent.)