Question

Problem 4-20
Amortization Schedule

Consider a $10,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 7%.

1. Set up an amortization schedule for the loan. Round your answers to the nearest cent. Enter "0" if required

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

   
   
2. How large must each annual payment be if the loan is for $20,000? Assume that the interest rate remains at 7% and that the loan is still paid off over 5 years. Round your answer to the nearest cent.
   $  
   
3. How large must each payment be if the loan is for $20,000, the interest rate is 7%, 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?
   -Select-VIVIIIIIIItem 26
   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.

Answer 1

a

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

10000= Cash Flow*((1-(1+ 7/100)^-5)/(7/100))

Cash Flow = 2438.91

	Annual rate(M)=	yearly rate/1=	7.00%	Annual payment=	2438.91
Year	Beginning balance (A)	Annual payment	Interest = M*A	Principal paid	Ending balance
1	10000.00	2438.91	700.00	1738.91	8261.09
2	8261.09	2438.91	578.28	1860.63	6400.46
3	6400.46	2438.91	448.03	1990.87	4409.59
4	4409.59	2438.91	308.67	2130.24	2279.35
5	2279.35	2438.91	159.55	2279.35	0.00

Where

Interest paid = Beginning balance * Annual interest rate

Principal = Annual payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Year ending balance

b

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

20000= Cash Flow*((1-(1+ 7/100)^-5)/(7/100))

Cash Flow = 4877.81

c

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

20000= Cash Flow*((1-(1+ 7/100)^-10)/(7/100))

Cash Flow = 2847.55

d