2 2 amortization

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2 2 amortization

  1. 1. Amortization
  2. 2. <ul><li>Amortization – a debt-repayment scheme wherein the original amount borrowed is repaid by making equal payments periodically </li></ul><ul><li>In amortization problems, we usually want to find the following values: </li></ul><ul><ul><li>Periodic payment </li></ul></ul><ul><ul><li>Outstanding principal at the end of any period </li></ul></ul><ul><ul><li>Interest payment for any period </li></ul></ul><ul><ul><li>Principal repayment for any period </li></ul></ul><ul><ul><li>Final irregular payment, if there is any </li></ul></ul>
  3. 3. <ul><li>Outstanding principal – refers to the amount of debt still unpaid </li></ul><ul><li>Amortization schedule – a table which shows how a debt is completely repaid through periodic payments, parts of which go to interest payments and principal repayments </li></ul>
  4. 5. <ul><li>Formulas: </li></ul><ul><li>Periodic payment </li></ul><ul><li>Outstanding principal </li></ul>
  5. 6. <ul><li>Formulas: </li></ul><ul><li>Interest payment </li></ul><ul><li>Principal repayment </li></ul><ul><li>Total interest (if all payments are regular) </li></ul>
  6. 7. <ul><li>3. Find R given A = Php 2.75M , j = 8% , m = 1 , and t = 12 years. </li></ul>
  7. 8. <ul><li>5. Find OB 115 given R = Php 17,315 , i = 1% , and n = 180 . </li></ul>
  8. 9. <ul><li>9. Find OB 42 given A = Php 1.9M , R = Php 21,525 , j = 10% , and m = 4 . </li></ul>
  9. 10. <ul><li>17. A loan is to be amortized via equal payments of Php119,764.71 each at the end of six months for 9 years. If the interest is based on 10% compounded semi-annually, find </li></ul><ul><li>a) the original amount of the loan </li></ul><ul><li>b) outstanding principal after the 8 th payment </li></ul><ul><li>c) outstanding principal after the 8 th year. </li></ul>
  10. 11. <ul><li>17. A loan is to be amortized via equal payments of Php119,764.71 each at the end of six months for 9 years. If the interest is based on 10% compounded semi-annually, find </li></ul><ul><li>a) the original amount of the loan </li></ul>
  11. 12. <ul><li>17. A loan is to be amortized via equal payments of Php119,764.71 each at the end of six months for 9 years. If the interest is based on 10% compounded semi-annually, find </li></ul><ul><li>b) outstanding principal after the 8 th payment </li></ul>
  12. 13. <ul><li>17. A loan is to be amortized via equal payments of Php119,764.71 each at the end of six months for 9 years. If the interest is based on 10% compounded semi-annually, find </li></ul><ul><li>c) outstanding principal after the 8 th year. </li></ul>
  13. 14. <ul><li>19. Goriotik obtains a Php13M bank loan at 12% interest compounded semi-annually to construct another studio. The company repays the loan by paying Php0.5M every 6 months. What is the outstanding principal after the 10 th payment? </li></ul>
  14. 15. <ul><li>21. A Php1.75M loan is to be repaid through annual payments of Php360,000. Construct an amortization schedule up to the end of the third period if effective interest rate is 9%. </li></ul>
  15. 16. Period Regular payment Interest payment Principal repayment Outstanding balance
  16. 17. Period Regular payment Interest payment Principal repayment Outstanding balance 0 1,750,000 1 2 3
  17. 18. Period Regular payment Interest payment Principal repayment Outstanding balance 0 1,750,000 1 360,000 157,500 202,500 1,547,500 2 3
  18. 19. Period Regular payment Interest payment Principal repayment Outstanding balance 0 1,750,000 1 360,000 157,500 202,500 1,547,500 2 360,000 139,275 220,725 1,326,775 3
  19. 20. Period Regular payment Interest payment Principal repayment Outstanding balance 0 1,750,000 1 360,000 157,500 202,500 1,547,500 2 360,000 139,275 220,725 1,326,775 3 360,000 119,409.75 240,590.25 1,086,184.75
  20. 21. <ul><li>25. A loan of Php400,000 with interest at 8% payable semi-annually is to be amortized through equal semi-annual payments for 5 years. </li></ul><ul><li>a) Find the amount of each semi-annual payment. </li></ul><ul><li>b) How much of the 6 th payment goes to interest payment? How much is allocated for repayment of principal? </li></ul><ul><li>c) How much is the total interest paid? </li></ul>
  21. 22. <ul><li>25. A loan of Php400,000 with interest at 8% payable semi-annually is to be amortized through equal semi-annual payments for 5 years. </li></ul><ul><li>a) Find the amount of each semi-annual payment. </li></ul>
  22. 23. <ul><li>25. A loan of Php400,000 with interest at 8% payable semi-annually is to be amortized through equal semi-annual payments for 5 years. </li></ul><ul><li>b) How much of the 6 th payment goes to interest payment? How much is allocated for repayment of principal? </li></ul>
  23. 24. <ul><li>25. A loan of Php400,000 with interest at 8% payable semi-annually is to be amortized through equal semi-annual payments for 5 years. </li></ul><ul><li>c) How much is the total interest paid? </li></ul>
  24. 25. <ul><li>27. How much will be the quarterly amortization for a Php1.34M loan with interest at 10% converted quarterly for a term of 6 years? How much interest will be paid on the 4th payment? What is the outstanding principal in 5 years? </li></ul>
  25. 26. <ul><li>27. How much will be the quarterly amortization for a Php1.34M loan with interest at 10% converted quarterly for a term of 6 years? How much interest will be paid on the 4th payment? What is the outstanding principal in 5 years? </li></ul>
  26. 27. <ul><li>27. How much will be the quarterly amortization for a Php1.34M loan with interest at 10% converted quarterly for a term of 6 years? How much interest will be paid on the 4th payment? What is the outstanding principal in 5 years? </li></ul>
  27. 28. <ul><li>27. How much will be the quarterly amortization for a Php1.34M loan with interest at 10% converted quarterly for a term of 6 years? How much interest will be paid on the 4th payment? What is the outstanding principal in 5 years? </li></ul>
  28. 29. <ul><li>29. To restructure a loan payment supposedly due now, a debtor agrees to Php111,500 payment at the end of each 6 months for 4 years including interest payments at 7%, m = 2. </li></ul><ul><li>a) Determine the outstanding principal after the 4 th payment. </li></ul><ul><li>b) What part of the 7 th payment is interest payment? </li></ul><ul><li>c) What part of the 7 th payment is allotted for principal repayment? </li></ul>
  29. 30. <ul><li>29. To restructure a loan payment supposedly due now, a debtor agrees to Php111,500 payment at the end of each 6 months for 4 years including interest payments at 7%, m = 2. </li></ul><ul><li>a) Determine the outstanding principal after the 4 th payment. </li></ul>
  30. 31. <ul><li>29. To restructure a loan payment supposedly due now, a debtor agrees to Php111,500 payment at the end of each 6 months for 4 years including interest payments at 7%, m = 2. </li></ul><ul><li>b) What part of the 7 th payment is interest payment? </li></ul>
  31. 32. <ul><li>29. To restructure a loan payment supposedly due now, a debtor agrees to Php111,500 payment at the end of each 6 months for 4 years including interest payments at 7%, m = 2. </li></ul><ul><li>c) What part of the 7 th payment is allotted for principal repayment? </li></ul>
  32. 33. <ul><li>Final irregular payment </li></ul><ul><ul><li>When n is not an integer, a smaller final payment is needed to completely settle a debt </li></ul></ul><ul><ul><li>Unless specified, this final payment is made one period after the last regular payment </li></ul></ul><ul><li>Formulas: </li></ul>
  33. 34. <ul><li>1. A debt of Php450,000 will be amortized by semi-annual payments of Php58,000 for as long as necessary. If interest is paid at 5 ½% compounded semi-annually, find </li></ul><ul><li>a) the number of full payments </li></ul><ul><li>b) the final or concluding payment </li></ul>
  34. 35. <ul><li>1. A debt of Php450,000 will be amortized by semi-annual payments of Php58,000 for as long as necessary. If interest is paid at 5 ½% compounded semi-annually, find </li></ul><ul><li>a) the number of full payments </li></ul>
  35. 36. <ul><li>1. A debt of Php450,000 will be amortized by semi-annual payments of Php58,000 for as long as necessary. If interest is paid at 5 ½% compounded semi-annually, find </li></ul><ul><li>b) the final or concluding payment </li></ul>
  36. 37. <ul><li>3. A Php25,000 office equipment is bought with a downpayment of Php5,000 and monthly installments of Php2,000. If the buyer pays 18% interest compounded monthly, </li></ul><ul><li>a) how much will be the outstanding principal after the 5 th installment? </li></ul><ul><li>b) how much interest is paid on the 9 th installment? </li></ul><ul><li>c) how much of the principal has been reduced by the 7 th installment? </li></ul><ul><li>d) what is the final irregular installment? </li></ul>
  37. 38. <ul><li>3. A Php25,000 office equipment is bought with a downpayment of Php5,000 and monthly installments of Php2,000. If the buyer pays 18% interest compounded monthly, </li></ul><ul><li>a) how much will be the outstanding principal after the 5 th installment? </li></ul>
  38. 39. <ul><li>3. A Php25,000 office equipment is bought with a downpayment of Php5,000 and monthly installments of Php2,000. If the buyer pays 18% interest compounded monthly, </li></ul><ul><li>b) how much interest is paid on the 9 th installment? </li></ul>
  39. 40. <ul><li>3. A Php25,000 office equipment is bought with a downpayment of Php5,000 and monthly installments of Php2,000. If the buyer pays 18% interest compounded monthly, </li></ul><ul><li>c) how much of the principal has been reduced by the 7 th installment? </li></ul>
  40. 41. <ul><li>3. A Php25,000 office equipment is bought with a downpayment of Php5,000 and monthly installments of Php2,000. If the buyer pays 18% interest compounded monthly, </li></ul><ul><li>d) what is the final irregular installment? </li></ul>

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