1. Amortization

2. If a loan (debt) is repaid on installments (usually in equal amount), then the loan is said to be repaid by amortization method.
Amortization – a debt-repayment scheme wherein the original amount borrowed is repaid by making equal payments periodically
Each installment payment consists of payment of interest and repayment of principal.
All payments form an annuity whose present value is the original loan L.
original loan = L P R n
n-1
n-2 4 3 2 1
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3. Ex1 A man buys a color TV worth P48,000
Ex1 A man buys a color TV worth P48,000. It is to be amortized through 6 monthly installments starting the next month. If interest is charged at 14% compounded monthly, find the monthly payment.
48,000 = P R 6 5 4 3 2 1
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4. Any remaining debt after k payments is called outstanding balance ( ) or outstanding liability or remaining liability ( ) or outstanding principal.
OBk
RLk
Outstanding balance (OB) or Remaining Liability (RL) – refers to the amount of debt still unpaid
Methods of finding or
(i) Prospective Method (n is known)
(ii) Retrospective Method (n is not known)
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5. If a loan L is to be repaid by n payments of R, the outstanding balance just after the kth payment denoted by or , is the present value of the (n-k) payments still to be made.
Pn-k
remaining (n-k) payments still to be made
original loan = L n
(n-1)
(n-2)
k-1
k-2 2 1 R k
k+1
k+2
k payments already made
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6. obligations = payments
If total number of payments (n) is NOT KNOWN, then we use retrospective method to find the outstanding balance
or remaining liability after k payments .
obligations = payments
remaining debt on the kth period
Value of k payments on the kth period Fk
remaining unknown number of payments
k payments already made
k-1
k-2 2 1 R k
k+1
k+2 CD
original loan = L
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7. b) outstanding principal after the 8th payment
Ex 2 A loan is to be amortized via equal payments of P100,000 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 8th payment
c) outstanding principal after the 8th year.
original loan = L = P 18 17 16 7 6 2 1 R 8 9 10
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8. Ex 2 A loan is to be amortized via equal payments of P100,000 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 8th payment
P10
remaining (18-8) payments still to be made 18 17 16 7 6 2 1 R 8 9 10
1,168, = L
8 payments already made
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9. Ex 2 A loan is to be amortized via equal payments of P100,000 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 8th year
remaining (18-16)
payments P2 18 17 16 7 6 2 1 R 8 9 10
1,168, = L
16 payments already made
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10. Ex 3 A debt is being repaid at P5000 every 6 months.
The interest is 18% compounded semi-annually. If the outstanding liability after the 5th payment is P24,000, find the original loan.
5 payments already made F5 6 5 2 1 7
5000
original loan = L = A
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11. Ex 4 Goriotik obtains a P13M bank loan at 12% interest compounded semi-annually to construct another studio. The company repays the loan by paying P0.5M every 6 months. What is the outstanding principal after the 10th payment?
F10
10 payments already made 8 7 2 1 9
0.5M 10 11
P13,000,000 = L = A
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12. If a loan (debt) is amortized, each installment payment is broken down into interest payment and repayment of principal.
A table showing the breakdown of each periodic payment into interest payment (I) and repayment of principal (RP) is known as an amortization schedule.
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13. Outstanding balance/principal
Periodic payment
Outstanding balance/principal
Interest payment on the kth period
Repayment of Principal on the kth period
Outstanding balance at the end of kth period

14. 5. Construct an amortization schedule for a loan of P2000 to be amortized through 5 semi-annual payments if interest is charged at 16% compounded semi-annually.
PERIOD R 1 2 3 4 5

15. Construct an amortization schedule for a loan of P2000 to be amortized through 5 semi-annual payments if interest is charged at 16% compounded semi-annually.
PERIOD R 1 2 3 4 5

16. Construct an amortization schedule for a loan of P2000 to be amortized through 5 semi-annual payments if interest is charged at 16% compounded semi-annually.
PERIOD R 1 2 3 4 5

17. Construct an amortization schedule for a loan of P2000 to be amortized through 5 semi-annual payments if interest is charged at 16% compounded semi-annually.
PERIOD R 1 2 3 4 5

18. Construct an amortization schedule for a loan of P2000 to be amortized through 5 semi-annual payments if interest is charged at 16% compounded semi-annually.
PERIOD R 1 2 3 4 5

19. Construct an amortization schedule for a loan of P2000 to be amortized through 5 semi-annual payments if interest is charged at 16% compounded semi-annually.
PERIOD R 1 2 3 4 5

20. Interest payment decreases as repayment of principal increases.
PERIOD R 1 2 3 4 5
TOTAL
Interest payment decreases as repayment of principal increases.

21. PERIOD R 1 2 3 4 5
TOTAL

22. a) Find the amount of each quarterly payment.
Ex6. A loan of P25,000 with interest at 18% is payable quarterly for 6.5 years.
a) Find the amount of each quarterly payment.
b) How much of the 16th payment goes to interest payment?
c) By how much will principal be lessened by 16th quarter?
d) How much is the total interest paid?
25,000 = L=
P26 26 25 24 7 6 2 1 R 8 9 10
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23. b) How much of the 16th payment goes to interest payment?
Ex6. A loan of P25,000 with interest at 18% is payable quarterly for 6.5 years.
b) How much of the 16th payment goes to interest payment?
P11
remaining (26-15) payments still to be made 26 25 24 15 14 2 1 R 16 17 18
25,000 = L
15 payments already made
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24. c) By how much will principal be lessened by 16th quarter?
Ex6. A loan of P25,000 with interest at 18% is payable quarterly for 6.5 years.
c) By how much will principal be lessened by 16th quarter?
d) How much is the total interest paid? 26 25 24 15 14 2 1 R 16 17 18
25,000 = L
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25. Ex7. A P50,000 loan is amortized by 25 installments made every 6 months. The interest rate is 15% converted semi-annually.
a) What is the semi-annual payment?
b) What part of the 12th payment is used to pay interest?
c) How much of the principal is repaid on the 12th period?
d) What is the total interest paid in discharging the debt?
50,000 = L=
P25 25 24 23 9 8 2 1 R 10 11 12
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26. Ex7. A P50,000 loan is amortized by 25 installments made every 6 months. The interest rate is 15% converted semi-annually.
b) What part of the 12th payment is used to pay interest?
P14
remaining (25-11) payments still to be made 25 24 23 9 8 2 1 R 10 11 12
50,000 = L
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27. c) How much of the principal is repaid on the 12th period?
Ex7. A P50,000 loan is amortized by 25 installments made every 6 months. The interest rate is 15% converted semi-annually.
c) How much of the principal is repaid on the 12th period?
d) What is the total interest paid in discharging the debt? 25 24 23 9 8 2 1 R 10 11 12
50,000 = L
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