Consider a $$15,000$ loan to be repaid in equal installments at the end of each of the next $5$ years. The interest rate $8\%.$

a$.$ Set up an amortization schedule for the loan. Do not round intermediate calculations. Round your answers to the nearest cent. If no entry is required, enter $"0".$

$\backslash$table$[[$Year$,,$Payment,Repayment Interest,Repayment of Principal,Balance$],[1,$$$,$$$,$$$,$$$,],[2,$$$,$$$,$$$,$$$,],[3,$$$,$$$,$$$,$$$,],[4,$$$,$$$,$$$,$$$,],[5,$$$,$$$,$$$,$$$,],[$Total$,$$$,$$$,$$$,,]]$

round intermediate calculations. Round your answer to the nearest cent.

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c$.$ How large must each payment be if the loan is for $$30,000,$ the interest rate is $8\%,$ and the loan is paid off in equal installments at the end of $10$ years This loan is for the same amount as the loan in part b$,$ but the payments are spread out over twice as many periods. Do not round intermediate calculations. Round your answer to the nearest cent.

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Why are these payments not half as large as the payments on the loan in part b$?$

I. Because the payments are spread out over a longer time period, more principal must be paid on the loan, which raises the amount of each payment.

II$.$ Because the payments are spread out over a longer time period, less interest is paid on the loan, which raises the amount of each payment.

III. Because the payments are spread out over a longer time period, less interest is paid on the loan, which lowers the amount of each payment.

IV$.$ Because the payments are spread out over a shorter time period, more interest is paid on the loan, which lowers the amount of each payment.

V$.$ Because the payments are spread out over a longer time period, more interest must be paid on the loan, which raises the amount of each payment.