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2 2 amortization

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  • 1. Amortization
  • 2.
    • Amortization – a debt-repayment scheme wherein the original amount borrowed is repaid by making equal payments periodically
    • In amortization problems, we usually want to find the following values:
      • Periodic payment
      • Outstanding principal at the end of any period
      • Interest payment for any period
      • Principal repayment for any period
      • Final irregular payment, if there is any
  • 3.
    • Outstanding principal – refers to the amount of debt still unpaid
    • 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
  • 4.  
  • 5.
    • Formulas:
    • Periodic payment
    • Outstanding principal
  • 6.
    • Formulas:
    • Interest payment
    • Principal repayment
    • Total interest (if all payments are regular)
  • 7.
    • 3. Find R given A = Php 2.75M , j = 8% , m = 1 , and t = 12 years.
  • 8.
    • 5. Find OB 115 given R = Php 17,315 , i = 1% , and n = 180 .
  • 9.
    • 9. Find OB 42 given A = Php 1.9M , R = Php 21,525 , j = 10% , and m = 4 .
  • 10.
    • 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
    • a) the original amount of the loan
    • b) outstanding principal after the 8 th payment
    • c) outstanding principal after the 8 th year.
  • 11.
    • 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
    • a) the original amount of the loan
  • 12.
    • 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
    • b) outstanding principal after the 8 th payment
  • 13.
    • 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
    • c) outstanding principal after the 8 th year.
  • 14.
    • 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?
  • 15.
    • 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%.
  • 16. Period Regular payment Interest payment Principal repayment Outstanding balance
  • 17. Period Regular payment Interest payment Principal repayment Outstanding balance 0 1,750,000 1 2 3
  • 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
  • 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
  • 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
  • 21.
    • 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.
    • a) Find the amount of each semi-annual payment.
    • b) How much of the 6 th payment goes to interest payment? How much is allocated for repayment of principal?
    • c) How much is the total interest paid?
  • 22.
    • 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.
    • a) Find the amount of each semi-annual payment.
  • 23.
    • 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.
    • b) How much of the 6 th payment goes to interest payment? How much is allocated for repayment of principal?
  • 24.
    • 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.
    • c) How much is the total interest paid?
  • 25.
    • 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?
  • 26.
    • 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?
  • 27.
    • 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?
  • 28.
    • 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?
  • 29.
    • 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.
    • a) Determine the outstanding principal after the 4 th payment.
    • b) What part of the 7 th payment is interest payment?
    • c) What part of the 7 th payment is allotted for principal repayment?
  • 30.
    • 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.
    • a) Determine the outstanding principal after the 4 th payment.
  • 31.
    • 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.
    • b) What part of the 7 th payment is interest payment?
  • 32.
    • 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.
    • c) What part of the 7 th payment is allotted for principal repayment?
  • 33.
    • Final irregular payment
      • When n is not an integer, a smaller final payment is needed to completely settle a debt
      • Unless specified, this final payment is made one period after the last regular payment
    • Formulas:
  • 34.
    • 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
    • a) the number of full payments
    • b) the final or concluding payment
  • 35.
    • 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
    • a) the number of full payments
  • 36.
    • 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
    • b) the final or concluding payment
  • 37.
    • 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,
    • a) how much will be the outstanding principal after the 5 th installment?
    • b) how much interest is paid on the 9 th installment?
    • c) how much of the principal has been reduced by the 7 th installment?
    • d) what is the final irregular installment?
  • 38.
    • 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,
    • a) how much will be the outstanding principal after the 5 th installment?
  • 39.
    • 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,
    • b) how much interest is paid on the 9 th installment?
  • 40.
    • 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,
    • c) how much of the principal has been reduced by the 7 th installment?
  • 41.
    • 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,
    • d) what is the final irregular installment?