amortization - fcampena · amortization method. each installment payment consists of payment of...

Amortization

Amortization

Amortization

R

nn-1n-243210

R R R R R R

P

S.Y.Tan

If a loan (debt) is repaid on installments (usually in equal amount), then the loan is said to be repaid by amortization method.

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

Amortization – a debt-repayment scheme wherein the original amount borrowed is repaid by making equal payments periodically

Amortization

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

6543210

R R R RR

S.Y.Tan

AmortizationS.Y.Tan

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)

Amortization

k payments already made

remaining (n-k) payments still to be made

S.Y.Tan

Pn-k

n(n-1)(n-2)k-1k-2210

R R R R R

k k+1 k+2

R R R R R

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.

original loan = L

Amortization

remaining unknown number of payments

S.Y.Tan

Fk

k-1k-2210

R R

k k+1 k+2

R R R R R

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 .

original loan = L

CD

Value of k payments on the kth period

remaining debt on the kth period

k payments already made

obligations = payments

AmortizationS.Y.Tan

18171676210

R R R R R

8 9 10

R R R R R

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

AmortizationS.Y.Tan

18171676210

R R R R R

8 9 10

R R R R R




b) outstanding principal after the 8th payment

1,168,958.69 = L

remaining (18-8) payments still to be made

8 payments already made

P10

AmortizationS.Y.Tan

18171676210

R R R R R

8 9 10

R R R R R




c) outstanding principal after the 8th year

1,168,958.69 = L

remaining (18-16)payments


P2

AmortizationS.Y.Tan

65210 7

5000 5000 5000 5000 5000

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.

original loan = L = A

5 payments already madeF5

AmortizationS.Y.Tan

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?

P13,000,000 = L = A

10 payments already made F10

87210 9

0.5M 0.5M 0.5M 0.5M 0.5M

10 11

0.5M 0.5M

AmortizationS.Y.Tan

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.

Amortization

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

Amortization

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

0

1

2

3

4

5

Amortization

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

0

1

2

3

4

5

Amortization

Interest payment decreases as repayment of principal increases.

PERIOD R

0

1

2

3

4

5

TOTAL

Amortization

PERIOD R

0

1

2

3

4

5

TOTAL

AmortizationS.Y.Tan

26252476210

R R R R R

8 9 10

R R R R R

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

AmortizationS.Y.Tan

2625241514210

R R R R R

16 17 18

R R R R R



b) How much of the 16th payment goes to interest payment?

P11

25,000 = L

remaining (26-15) payments still to be made


AmortizationS.Y.Tan

2625241514210

R R R R R

16 17 18

R R R R R



c) By how much will principal be lessened by 16th quarter?

d) How much is the total interest paid?

25,000 = L

AmortizationS.Y.Tan

25242398210

R R R R R

10 11 12

R R R R R

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

AmortizationS.Y.Tan

25242398210

R R R R R

10 11 12

R R R R R



b) What part of the 12th payment is used to pay interest?

50,000 = L

P14remaining (25-11) payments still to be made

AmortizationS.Y.Tan

25242398210

R R R R R

10 11 12

R R R R R



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

AmortizationS.Y.Tan

Ex8. A loan of P22,500 is amortized at P2000 every 6

months and a final payment, with interest at 16%

compounded semi-annually.

a) Find outstanding liability at the end of 10 years.

b) How much of the 15th payment is interest payment and

how much is the principal repaid?

AmortizationS.Y.Tan




b) How much of the 15th payment is interest payment and

how much is the principal repaid?

AmortizationS.Y.Tan

Ex1. A P7500 loan is to be amortized at P1500 each quarter and a final

irregular payment made 3 months after last regular payment. If interest

is 12% converted quarterly.

a) How many regular payments are needed?

b) When is the final payment due?

c) How much is the final payment?

d) Construct an amortization schedule for it.

AMORTIZATION WITH FINAL IRREGULAR PAYMENT

Amortization

150

0

76543210

1500 1500

S.Y.Tan

Ex1. A P7500 loan is to be amortized at P1500 each quarter and a final

irregular payment made 3 months after last regular payment. If interest

is 12% converted quarterly.

b) When is the final payment due?

c) How much is the final payment?

a) There should be 5 regular quarterly payments of P1500.

b) He will complete his full payment (final irregular payment x ) on the 6th quarter.

7500=L

Remaining balance after last regular payment of P1500 (end of 5th quarter)

Final irregular payment if it is to made one period after the last regular payment of P1500.

Amortization

0

1

2

3

4

5

6

Total

AmortizationS.Y.Tan




a) Find the final payment and when is it due?

b) What is the total interest paid in discharging the loan?

AmortizationS.Y.Tan




a) Find the final payment and when is it due?


Final irregular payment is due at the end of 30th

semi-annual period.

AmortizationS.Y.Tan





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