Amortization Schedule Set up an amortization schedule for a $50,000 loan to be r

Question

Amortization Schedule

Set up an amortization schedule for a $50,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 6%. Round your answers to the nearest cent. Enter "0" if required

How large must each annual payment be if the loan is for $100,000? Assume that the interest rate remains at 6% and that the loan is paid off over 5 years. Round your answer to the nearest cent.
$  

How large must each payment be if the loan is for $100,000, the interest rate is 6%, 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. 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 lowers the amount of each payment.
II. 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.
III. 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.
IV. 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.
V. 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.

Year Payment Repayment Interest Repayment of Principal Balance 1 $   $   $   $   2 $   $   $   $   3 $   $   $   $   4 $   $   $   $   5 $   $   $   $   Total $   $   $  

Explanation / Answer

Annuity ( Annual installment) = Loan / PVIFA 6%, 5 years = $ 50,000 / 4.2124 = $ 11,869.72

a. Amortization Schedule:

* $ 50,000 x 6% = $ 3,000

** $ ( 50,000 - 8,869.72) x 6% = $ 2,467.82

b. Annual payment at 6% payable annually over 5 years = $ 100,000 / 4.2124 = $ 23,739.44

c. If the loan is $ 100,000, the annual payment at 6% interest and payment period 10 years = $ 100,000 / 7.3601 = $ 13,586.77

d. The correct option is III.

Year Payment Payment of interest Repayment of principal Balance $ $ $ $ $ 50,000 1 11,869.72 3,000* 8,869.72 41,130.28 2 11,869.72 2,467.82** 9401.90 31,728.38 3 11,869.72 1,903.70 9,966,02 21,762.36 4 11,869.72 1,305.74 10,563.98 11,198.38 5 11,869.72 671.34 11,198.38 Total 9,348.60 50,000

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