Please explain everything in detail please.$[$Amortization Schedule$]$

Consider a $$50,000$ loan to be repaid in equal installments at the end of each of the next $5$ years. The interest rate is $8\%.$

a$.$ Set up an amortization schedule for the loan. Do not round intermediate calculations. Round your answers to the nearest cent. If your answer is zero, enter $"0".$

b$.$ How large must each annual payment be if the loan is for $$100,000?$ Assume that the interest rate remains at $8\%$ and that the loan is still paid off over $5$ years. Do

not round intermediate calculations. Round your answer to the nearest cent.

$

c$.$ How large must each payment be if the loan is for $$100,000,$ the interest rate is $8\%,$ and the loan is paid off in equal installments at the end of each of the next $10$

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.

$

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, less interest is 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 lowers the amount of each payment.

III. 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.

IV$.$ 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.

V$.$ 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.