After negotiating, you agree to a final price of $$49,244$ for a new car including tax, tags, and fees. You have saved $$6,077$ for the purchase, and will borrow the remainder at a rate of $5\mathrm{.}24\%$ APR compounded monthly. The loan requires you to make equal payments for the next $72$ months with the first payment due next month. What will be your monthly loan payment?

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Your client has $$15,966$ already in a retirement account, and she plans to add a $$9,745$ deposit one year from today, and increase that annual deposit by $2\%$ per year ending $35$ years from today $($so that there will be $35$ annual deposits$).$ Considering her current savings and future deposits, what will be her retirement account balance in $35$ years if the account is expected to earn an effective annual rate of $9\mathrm{.}81\%?$

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