Jan sold her house on December $31$ and took a $$50,000$ mortgage as part of the payment. The $10-$year mortgage has a $6\%$ nominal interest rate, but it calls for semiannual

payments beginning next June $30.$ Next year Jan must report on Schedule B of her IRS Form $1040$ the amount of interest that was included in the two payments she

received during the year.

a$.$ What is the dollar amount of each payment Jan receives? Round your answer to the nearest cent.

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b$.$ How much interest was included in the first payment? Round your answer to the nearest cent.

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How much repayment of principal was included? Do not round intermediate calculations. Round your answer to the nearest cent.

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How do these values change for the second payment?

I. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal increases.

II$.$ The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal decreases.

III. The portion of the payment that is applied to interest and the portion of the payment that is applied to principal remains the same throughout the life of the loan.

IV$.$ The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal also declines.

V$.$ The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal also increases.

c$.$ How much interest must Jan report on Schedule B for the first year? Do not round intermediate calculations. Round your answer to the nearest cent.

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Will her interest income be the same next year?

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d$.$ If the payments are constant, why does the amount of interest income change over time?

I. As the loan is amortized $($paid off$),$ the beginning balance, hence the interest charge, increases and the repayment of principal increases.

II$.$ As the loan is amortized $($paid off$),$ the beginning balance, hence the interest charge, declines and the repayment of principal increases.

III. As the loan is amortized $($paid off$),$ the beginning balance, hence the interest charge, declines and the repayment of principal declines.

IV$.$ As the loan is amortized $($paid off$),$ the beginning balance, hence the interest charge, increases and the repayment of principal declines.

V$.$ As the loan is amortized $($paid off$),$ the beginning balance declines, but the interest charge and the repayment of principal remain the same.