The answer is shown below in the picture. But I need to know how they solved it.

Suppose you are a manager for a certain company. You earn $50,000 per year and are in the 28% federal income tax bracket. Each year you contribute $4,500 tax free to your individual retirement account, IRA. The account earns 7% annual interest. In addition, the amount of tax that you save each year by making these "pre-tax" contributions is invested in a taxable aggressive growth mutual fund averaging 17%.

(a) How much tax do you save (in $) each year by making the retirement fund contributions?

(b) using Table 12-1, how much will the retirement fund be worth (in $) in 30 years? ( Round you answer to the nearest cent.)

(c) Although the income from this investment is taxable each year, using Table 12-1, how much will the "tax savings" fund be worth (in $) in 30 years? ( Round your answer to the nearest cent.)

Barble and 70se are married. Last year 8arbie earned $33,400 and bose earned $27,600 in wages. Addrional tax information for the year is as foloms: foterest earned: 57,000 ; alfmocy paid: $5,700; contributions to IRA retirement fund: 52,200; state and locat income taxes paid $6,200; contributions to charity: $2, 700 . The following table gives the standard defuction for various filing statuses. standard Dedections Find the taxable income if they file a joint return. \begin{tabular}{|r|} \hline$31,900 \\ \hline 535,000 \\ \hline 539,900 \\ 541,200 \\ \hline \end{tabular} Future Value (Amount) of an Ordinary Annuity of The values in Table 12-1 were generated by the formula i(1+i)n1 and rounded to five decimal places, where i is the interest rate per period and n is the total number of periods. rate per period and n is the total number of periods