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Chapter 14

Amortiz. of. ation. Loans. Chapter 14. Learning Objectives. Calculate. After completing this chapter, you will be able to:. …the principal balance after any payment using both the Prospective Method and the Retrospective Method. LO 1. LO 2.

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Chapter 14

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  1. Amortiz of ation Loans Chapter14

  2. Learning Objectives Calculate After completing this chapter, you will be able to: …the principal balance after any paymentusing both the Prospective Method and the Retrospective Method LO 1. LO 2. … the final loan payment when it differs from the others LO 3. … the principaland interest components of any payment And…

  3. Learning Objectives Calculate LO 4. … mortgage payments for the initial loan and its renewals … mortgage loan balances and amortization periods to reflect prepayments of principal LO 5.

  4. CPT ENTER 2nd 2nd FV I/Y PV N PMT 12 P/Y QUIT Q A $20,000 mortgage loan at 9%compounded monthly requires monthly payments during its 20-year amortization period. LO 1. (1) Calculate the monthly payment. (2) Using the monthly payment from part (1), calculate the PVof all payments. (3) Why does the answer in (2) differ from $20,000? PV = $20000 FV = 0 n =12* 20= 240 1. PMT =-179.95 240 20 000 9 0 2. & 3.

  5. Q CPT (2) Using the monthly payment from part (1), calculate the PVof all payments. (3) Why does the answer in (2) differ from $20,000? PV PMT 2. PV = ? FV = 0 n =12*20= 240 PMT=179.95 179.95 PV =20,000.5345 179.95 3. The difference of $0.5345 is due to rounding the monthly payment to the nearest cent!

  6. Q A $20,000 mortgage loan at 9%compounded monthly requires monthly payments during its 20-year amortization period. CPT PV N Step Step Now Calculate the exact balance after 5 years assuming the final payment will be adjusted for the effect of rounding the regular payment. Calculate the exact n for monthly payments of $179.95 to repay a $20,000 loan... 20 000 N =239.982

  7. Q A $20,000 mortgage loan at 9%compounded monthly requires monthly payments during its 20-year amortization period. CPT PV N Step - N =239.982 = Now Calculate the exact balance after 5 years assuming the final payment will be adjusted for the effect of rounding the regular payment. N =179.9821 P/V =17,741.05 After 5 years, 239.982 – 60 = 179.982 payments remain. Therefore, balance (after 5 years) = PV of 179.982payments of $179.95 60

  8. Consider that… An Original Loan = The PV of ALL of the Payments (discounted at the contractual rate of interest on the loan) Also, that… A Balance = The PV of the remainingPayments (discounted at the contractual rate of interest on the loan) Then…

  9. PV of the Balance just after the xth Payment PV of firstx Payments …this can be expressed as …the Statement of Economic Equivalence For a focal date of the original date of the loan, (Original Loan) Focal Date…

  10. Retrospective Retrospective Retrospective Methodfor Loan Balances FV of the Payments already made FV of theOriginal Loan FV of the Payments already made FV of theOriginal Loan of the xth payment, the Statement of Economic Equivalence becomes… Suppose we locate the Focal Date… Balance This is now rearranged to isolate the “Balance” Balance

  11. Retrospective Retrospective Retrospective Methodfor Loan Balances Application Prospective Methodfor Loan Balances … is based on PAYMENTSYET to be MADE!` whereas … is based on PAYMENTSALREADY MADE!`

  12. Q A $20,000 mortgage loan at 9%compounded monthly requires monthly payments of $179.95 during its 20-year amortization period. Calculate the exact balanceafter 5 years. Solve using… Retrospective Method Prospective Method Then compare…

  13. Retrospective Methodfor Loan Balances CPT ENTER 2nd 2nd FV I/Y PV N PMT 12 * 5 Years 12 P/Y QUIT Q A $20,000 mortgage loan at 9%compounded monthly requires monthly payments of $179.95 during its 20-year amortization period. Calculate the exact balanceafter 5 years. Balance = FV of $20,000 – FV of first 60 payments FV= 17,741.05 179.95 60 9 20,000

  14. Prospective Methodfor Loan Balances CPT ENTER 2nd 2nd FV I/Y PV N PMT 12 P/Y QUIT Q A $20,000 mortgage loan at 9%compounded monthly requires monthly payments of $179.95 during its 20-year amortization period. Calculate the exact balanceafter 5 years. Total payments= 12* 20 Years = 240 - 60 made = 180remaining Balance = PV of remaining 180 payments PV= 17,741.88 179.95 180 9 0

  15. Retrospective Methodfor Loan Balances FV= 17,741.05 Prospective Methodfor Loan Balances PV= 17,741.88 Comparison of Methods Difference ($0.83) is because the Prospective Methodassumes thatthe final payment is the same as all the others. The RetrospectiveMethod is based on payments already made.

  16. CPT ENTER 2nd 2nd FV I/Y PV N PMT 12 P/Y QUIT Q A $20,000 mortgage loan at 9%compounded monthly requires monthly payments of $179.95 during its 20-year amortization period. LO 2. Calculate the size of the final payment. Final Payment = (1+i) * (Balanceafter2nd to last payment) Balance after 239 payments = FV of $20,000 after 239 months – FV of 239 payments 179.95 FV= - 175.42 239 9 20,000 Final Payment = (1+0.09/12) * 175.42 = $176.74

  17. Steps CPT ENTER 2nd 2nd FV I/Y PV N PMT Balance after 10 payments 4 P/Y Needed QUIT 1. 2. 3. Q Meditech Laboratories borrowed $28,000 at 10%,compounded quarterly, to purchase new testing equipment. Paymentsof $1,500 are made every 3 months. A. Calculate the balance after the10th payment. B. Calculate the final payment. A. Balance after 10 payments = FV of $28,000 after 10 quarters – FV of 10 payments FV= - 19,037.29 1500 10 10 28,000 B.

  18. Q Steps • Meditech Laboratories borrowed $28,000 at 10%,compounded quarterly, to purchase new testing equipment. Paymentsof $1,500 are made every 3 months. • Calculate the balance after the10th payment. CPT CPT FV FV N N Calculate Calculate 1. …the number of payments 2. …the balanceafter the 2nd to last payment 3. B. Calculate the final payment. N = 25.457 FV = -673.79 0 25

  19. Q Meditech Laboratories borrowed $28,000 at 10%,compounded quarterly, to purchase new testing equipment. Paymentsof $1,500 are made every 3 months. A. Calculate the balance after the10th payment. B. Calculate the final payment. 3. …the final payment Step Calculate Final Payment = (1+0.10/4) * 673.79 = $690.63

  20. LO 3. A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate theinterest and principal components of the 29th payment. B. How much interest will be paid in the second year of the loan?

  21. Q A $9,500 personal loan at 10.5%compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate theinterest and principal components of the 29th payment. B. How much interest will be paid in the second year of the loan? CPT ENTER 2nd 2nd FV I/Y PV N PMT 12 P/Y QUIT First: … find the size of the monthly payment 9500 PV = n = 12(4) = 48 i = .105/12 PMT = - 243.23 48 10.5 9500 0

  22. Q A $9,500 personal loan at 10.5%compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate theinterest and principal components of the 29th payment. CPT FV N PMT First: … find the balanceafter the 28 payments A. PMT = - 243.23 FV = -4445.06 243.23 28 InterestComponent of Payment 29 = i* Balance after 28th payment = 0.105/12* 4445.06 = $38.89 Principal Component = PMT – InterestComponent = $243.23 - $38.89 = $204.34

  23. Q A $9,500 personal loan at 10.5%compounded monthly is to be repaid over a 4-year term by equal monthly payments. B. How much interest will be paid in the second year of the loan? CPT CPT FV FV N N Balance after 2 years Balance after 1 year First:… find the balanceafter 1 Year, and the balance after 2 Years B. FV = -7483.53 FV = -5244.84 12 24 TotalPrincipalpaid in year 2 = $7,483.53 - $5,244.84 = $2,238.69 TotalInterestpaid in year 2 = 12($243.23) - $2,238.69 = $680.07

  24. Mortgage … is a loansecuredby some physicalproperty

  25. Mortgage Loans …Basic Concepts and Definitions MORTGAGE APPLICATION Mortgage Lender Borrower …the borroweris called themortgagor …the lender is called themortgagee ...and

  26. Mortgage Loans …Basic Concepts and Definitions MORTGAGE APPLICATION Mortgage Face Valueof mortgage=originalprincipal amount Term… From …date on which loan advanced To…date on which the remainingPrincipal Balance is due and payable …most common periods are 20 and 25 years. Interest Rate …usually a lender will commit to a fixed interest rate for only a shorter period or term (6 monthsto 7 years)

  27. Illustration MORTGAGE APPLICATION Mortgage Graphic Illustrations A Mortgage Loan at 8.5%compounded semiannually with a 25-year amortization period

  28. Principal Component 100 90 80 70 Interest % 60 50 40 30 Interest Component 20 10 0 Years 0 5 10 15 20 25 The Composition of Mortgage Payments during a 25-year Amortization Approximately 40% Approximately 60% Year 14

  29. 100,000 90,000 80,000 70,000 60,000 Principal Balance $ 50,000 40,000 30,000 20,000 10,000 0 Years 0 5 10 15 20 25 Mortgages Declining Balance during a 25-year Amortization Principal declines slower in earlier years

  30. Mortgage Qualifying for One

  31. Qualifying for One …need to satisfy all 3 of the following Ratios… MORTGAGE APPLICATION Mortgage Mortgage Loan-to-Value Ratio (LVR) Gross Debt Service Ratio (GDS) Total Debt Service Ratio (TDS)

  32. Qualifying for One MORTGAGE APPLICATION Mortgage Mortgage Loan-to-Value Ratio (LVR) x Principal Amount of Loan £ 75% 100% Lending Value of Property Gross Debt Service Ratio (GDS) Total monthly payments for Mortgage, Property taxes, and Heat x £ 32% 100% Gross Monthly Income Total Debt Service Ratio (TDS) Total monthly payments for Mortgage, Property taxes, Heat and Other Debts x £ 40% 100% Gross Monthly Income

  33. You have saved $35,000for the down payment ona home. You want to know the maximum conventional mortgage loan for which you can qualify in order todetermine the highest price you can pay for a home. …gross monthly income is $3,200 … 18 payments of $300 per month remaining on a car loan … property taxes of $150 per month and heating costs of $100 per month … the bank has upper limits of 32% for the GDSRatio and 40% for the TDS Ratio Personal Data What maximum monthly mortgage payment do the GDS and TDS ratios permit?

  34. Total monthly payments for Mortgage, Property taxes, and Heat x £ 32% 100% Gross Monthly Income Gross Debt Service Ratio (GDS) Maximum Mortgage payment+ 150 + 100 = 32% $3,200 Maximum Mortgage payment= .32(3200) - 250 = $774

  35. Total monthly payments for Mortgage, Property taxes, Heat and Other Debts x £ 40% 100% Gross Monthly Income Total Debt Service Ratio (TDS) Maximum mortgage payment + 150 + 100+ 300 = 40% $3,200 Maximum Mortgage payment= .40(3200) - 550 = $730

  36. CPT ENTER ENTER 2nd 2nd FV I/Y PV N PMT Maximum Mortgage P/Y QUIT Q What is the maximum mortgage for which youqualify? Use a 25-year amortization and an interest rate of 8%compounded semiannuallyfor a five-year term. 12 P/Y= 12 C/Y= 2 P/V= 95,648.21 0 8 0 2 730 300

  37. x Principal Amount of Loan £ 75% 100% Lending Value of Property Q Based on a $35,00 down payment and the maximum loan possible, what is the highest price you can pay for a home? Loan-to-Value Ratio (LVR) = $95, 600 75% Minimum house value = $95, 648 = $127,530.67 Minimum house value 75% ...and

  38. Q Based on a $35,00 down payment and the maximum loan possible, what is the highest price you can pay for a home? $35,000 – 31,882 (Minimum down payment ) = over DP At this price, the minimum down payment is: $127,531– $95,648= $ 31,883 … the maximum price you can afford to payfor a home is… $3,118 + $127, 531 = $130,649

  39. MORTGAGE APPLICATION Mortgage Privileges & Penalties Common Prepayment

  40. Privileges & Common Prepayment Penalties Closed Partially Open Fully Open Limited penalty-free prepayment No restrictions or penalties on extra payments by the borrower! No prepaymentwithout a penalty Lump or Balloon Payments 10% or 15% of the original amount Increasing the Regular Payment…permanently Once a year by 10% or 15% “Double-Up” Pay twice the amount for any monthly payment

  41. Privileges & Common Prepayment Penalties Financial Penalties Example The most common prepayment penalty is the greater of: Contract provides for a financial penalty on any prepayment not specifically permitted Three months’interest on the amount prepaid, or The lender’s reduction in interest revenue fromthe prepaid amount(over the remainder of the mortgage’s term)

  42. Solving Steps The interest rate for the first 5-year term of a $100,000mortgage loan is 7.5%compounded semiannually. The mortgage requires monthly payments over a 25 year amortization period. The mortgage contract gives the borrower the right to prepayup to 10%of the original mortgage loan, once a year, without interest penalty. Suppose that, at the end of the second year of the mortgage, the borrower makes a prepayment of$10,000. LO 4. LO 5. • How much will the amortization period be shortened? • What will be the principal balance at the end of the five-year term?

  43. Steps Calculate Calculate Calculate Calculate 1. …the payments based on a 25-year amortization 2. …the balanceafter 24 payments 3. - Reduce this balance by $10,000 …the number of monthly paymentsneeded to pay off this new balance 4. …the reduction in the original 25-year amortization period 5.

  44. Steps CPT ENTER ENTER 2nd 2nd 1. …the payments based on a 25-year amortization FV I/Y PV N PMT Calculate monthly payment P/Y QUIT 2. 3. c = PV= 100,000 n = 25*12 = 300 i = .075/2 2/12 PMT= -731.55 12 100,000 2 300 7.5 0

  45. Steps CPT FV N balance after 24 payments PMT 2. …the balanceafter 24 payments balance after the prepayment Calculate - 3. - Reduce this balance by $10,000 = 4. 5. 87,007.25 FV= -97,007.25 24 731.55 10,000

  46. Steps CPT FV PV N 215 more payments to pay off the mortgage Calculate Calculate …the number of monthly paymentsneeded to pay off this new balance 4. …the reduction in the original 25-year amortization period 5. N= 214.60 87,007.25 0 …with the prepayment: 24 + 215 = 239 Total payments Therefore, 300-239 = 61 months saved... i.e.5 yrs 1 month

  47. Select: 4th Edition Student Centre Interactive Mortgage Payoff Chart…online www.mcgrawhill.ca/college/jerome/ Click On: Click On: Click On: Select: -or-

  48. This completes Chapter 14

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