Question

Problem 4-20 Amortization Schedule Consider a $10,000 loan to be repaid in equal installments at the...

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.

Homework Answers

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

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