Challenge Problem $14-21($Algo$)[$LU $14-2(1)]$ Peg Gasperoni bought a $\backslash (\backslash$$ $50,000\backslash )$ life insurance policy for $\backslash (\backslash$$ $310\backslash )$ per year. Ryan Life Insurance Company sent her the following billing instructions along with a premium plan example: "Your insurance premium notice will be mailed to you in a few days. You may pay the entire premium in full without a finance charge or you may pay the premium in installments after a down payment and the balance in monthly installments of $\backslash (\backslash$$ $80\backslash ).$ The finance charge will be added to the unpaid balance. The finance charge is based on an annual percentage rate of $18\backslash \%."$If the total policy premium is:And you put down:The balance subject to finance charge will be:The total number of monthly installments $(\backslash$$$30$ minimum$)$ will be:The monthly installment before adding the finance charge will be:The total installments will be:payment price will be: Peg feels that the finance charge of $\backslash (\backslash$$ $7\mathrm{.}11\backslash )$ is in error. a$.$ What is the actual finance charge for the first three months? Note: Round your answer to the nearest cent. Answer is complete but not entirely correct. b$.$ Is she correct?