3. Ammortization of Loan

8/9/2019 3. Ammortization of Loan

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Amortization

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McGraw-Hill Ryerson©

14 - 1

Chapter 14 of


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14 - 2

Calculate

Learnin !"#ecti$es

%the principal balance after any payment

using both the &rospecti$e

Metho' an' the Retrospecti$eMetho'

After completin this chapter( you will "e a"le to)

% the principal an' interest components of

any payment

An'%

An'%

% the final loan payment when it 'iffers

from the others

L! 1*

L! 1*

L! 2*

L! 2*

L! +*

L! +*


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14 - +

Learnin !"#ecti$es

Calculate

L! 4*

L! 4*

L! ,*

L! ,* % mortae loan "alances an'

amortization perio's to reflect

prepayments of principal

% mortae payments for the initial loan

an' its renewals


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14 - 4

A 2.(... mortae loan at /0 compoundedmonthly reuires monthly payments 'urin its

2.-year amortization perio'*

13 Calculate the monthly payment *23 sin the monthly payment from part 13(

calculate the &5 of all payments*+3 Why 'oes

the answer in 23 differ from 2.(...6

24./

.

2. ...

&M7 8 -19/*/,12

n 812: 2. 8 24.&5 8 2.... ;5 8 .

1*

1*

2*

2* <

< +*

+*

L! 1*

L! 1*


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14 - ,

23 sin the monthly payment from part 13(calculate the &5 of all payments*

+3 Why 'oes the answer in 23 differ from 2.(...6

2*

2*

+*

+*

19/*/,

19/*/,

n 812:2. 8 24.&5 8 6 ;5 8 . &M7 8 19/*/,

&5 8 2.(...*,+4,

7he 'ifference of .*,+4, is 'ue to roun'in the

monthly payment to the nearest cent=

7he 'ifference of .*,+4, is 'ue to roun'in the

monthly payment to the nearest cent=


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14 - >

Calculate the exact balance after , years

assumin the final payment will "e a'#uste' for

the effect of roun'in the reular payment*






Calculate the exact n for monthly payments of19/*/, to repay a 2.(... loan***

2. ...? 8 2+/*/@2


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14 - 9









After , years( 2+/*/@2 >. 8 19/*/@2 payments remain*

7herefore( "alance after , years38 &5 of 19/*/@2 payments of 19/*/,

>.

? 8 2+/*/@2? 8 19/*/@21&B5 8 19(941*.,


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14 - @

An !riinal Loan 8

Consi'er that%Consi'er that%

7he &5 of ALL of the &ayments

discounted at the contractual

rate of interest on the loan3

Also( that%Also( that%

A alance 8 7he &5 of the remainin &ayments

discounted at the contractual

rate of interest on the loan3

7hen%7hen%


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14 - /

%this can "e eDpresse' as %the Statement of Economic Equivalence%this can "e eDpresse' as %the Statement of Economic Equivalence

!riinal Loan3

;ocal Eate%;ocal Eate%

&5 of first D

&ayments

&5 of the

alance #ust

after the Dth

&ayment

;or a focal 'ate of the oriinal 'ate of the loan(


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14 - 1.

of the Dth payment(

the Statement of Economic Equivalence becomes…

Retrospecti$e Metho' for Loan alances

Retrospecti$eRetrospecti$e

Fuppose we locate the ;ocal Eate%

alance

7his is now rearrane' to isolate the Balance

alance

;5 of the

!riinal Loan

;5 of the

&aymentsalrea'y ma'e

;5 of the

!riinal Loan

;5 of the

&ayments

alrea'y ma'e


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14 - 11


Retrospecti$eRetrospecti$e

% is "ase' on &AIMJ?7F ALREA! "AE#$

&rospecti$e Metho' for Loan alances

% is "ase' on &AIMJ?7F !E% to be "AE#$

ApplicationApplication


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14 - 12

&alculate the exact balance after ' years( &alculate the exact balance after ' years (

A 2.(... mortae loan at /0 compounded

monthly reuires monthly payments of 19/*/, 'urin its 2.-year amortization perio'*

Fol$e usin%

Retrospecti$e Metho'

&rospecti$e Metho'

7hen compare%


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14 - 1+





alance 8 ;5 of 2.(... ;5 of first )* payments

>.19/*/,

12

/

2.(...

12 : , Iears

12 : , Iears

;58 19(941*.,


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14 - 14

&rospecti$e Metho' for Loan alances




12: 2. Iears 8 24.12: 2. Iears 8 24.7otal payments +

[email protected]/*/,12

/

&58 19(941*@@

.

- >. ma'e 8 1@. remaininalance 8 &5 of remainin 1@. payments


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14 - 1,

Eifference , -*(./3 is "ecause the &rospecti$e Metho'

assumes that the final payment is the same as all the others(

7he Retrospecti$e Metho' is based on payments

already made (

;58 19(941*.,Retrospecti$e Metho'

for Loan alancesRetrospecti$e Metho'

for Loan alances

&58 19(941*@@&rospecti$e Metho' for Loan alances

&rospecti$e Metho'

for Loan alances

Comparison of Metho's

14 1>


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14 - 1>

;inal &ayment 8 1Ki 3 : alance after 2n' to last payment3

alance after 2+/ payments 8

;5 of 2.(... after 2+/ months ;5 of 2+/ payments

2+/

19/*/,

12/ ;58 - 19,*42

2.(...

;inal &ayment 8 1K.*./B123 : 19,*42

8 19>*94

8 19>*94

&alculate the si0e of the final payment( &alculate the si0e of the final payment (

A 2.(... mortae loan at /0 compoun'e'monthly reuires monthly payments of 19/*/,

'urin its 2.-year amortization perio'*L! 2*L! 2*

14 19


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14 - 19

Me'itech La"oratories "orrowe' -1.2*** at1.0( compoun'e' uarterly(to purchase new testin euipment*

&ayments of 1(,.. are ma'e e$ery + months*A* Calculate the "alance after the 1.th payment*

* Calculate the final payment*


&ayments of 1(,.. are ma'e e$ery + months*A* Calculate the "alance after the 1.th payment** Calculate the final payment*

alance after 1. payments 8 ;5 of 2@(... after 1. uarters ;5 of 1. payments

1.1,..

4

1.

;58 - 1/(.+9*2/

2@(...

A*

*2*2*1*1* +*+*

3eeded

Balance after

1. payments

Balance after

1. payments

14 1@


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14 - 1@





%the num"er of payments1*1* Calculate

.

? 8 2,*4,9;5 8 ->9+*9/

2,

%the "alance after the 2n' to last payment2*2* Calculate

+*+*


14 1/


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14 - 1/

%the final payment+*+* Calculate





&ayments of 1(,.. are ma'e e$ery + months*A* Calculate the "alance after the 1.th payment** Calculate the final payment*

;inal &ayment 8 1K.*1.B43 : >9+*9/

8 >/.*>+8 >/.*>+

14 2.


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14 - 2.

A 42'** personal loan at 1.*,0 compoun'e' monthly is to "e

repai' o$er a 4-year term "yeual monthly payments*

A* Calculate the interest an' principalcomponents of the 2/th payment*

* How much interest will "e pai' inthe secon' year of the loan6

L! +*L! +*

14 21


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14 - 21

A 42'** personal loan at 1.*,0 compoun'e'monthly is to "e repai' o$er a 4-year term

"y eual monthly payments*

A* Calculate the interest an' principal componentsof the 2/th payment* * How much interest will"e pai' in the secon' year of the loan6


"y eual monthly payments*A* Calculate the interest an' principal components

of the 2/th payment* * How much interest will"e pai' in the secon' year of the loan6

5irst6 … find the si0e of the monthly payment

&5 8 n 8 i 8/,.. 1243 8 4@ *1.,B12

4@

12

1.*,

&M7 8 - 24+*2+

/,.. .

14 22


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14 - 22



A* Calculate the interest an' principal componentsof the 2/th payment*


"y eual monthly payments*A* Calculate the interest an' principal components

of the 2/th payment*

A*

5irst6 … find the balance after the 1. payments

2@

&M7 8 - 24+*2+

24+*2+

;5 8 -444,*.>

nterest &omponent of &ayment 2/

8 .*1.,B12: 444,*.> 8 +@*@/

+ i : alance after 2@th payment

&rincipal &omponent 8 &M7 nterest &omponent

8 24+*2+ - +@*@/

8 2.4*+48 2.4*+4

14 2+


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14 - 2+



* How much interest will "e pai' in thesecon' year of the loan6


"y eual monthly payments** How much interest will "e pai' in the

secon' year of the loan6

5irst6… find the balance after 7 !ear 2 and the balance after 1 !ears

12

;5 8 -94@+*,+

%otal &rincipal paid in year 2 8 9(4@+*,+ - ,(244*@4

8 2(2+@*>/8 2(2+@*>/

24

;5 8 -,244*@4

%otal nterest paid in year 2 8 1224+*2+3 - 2(2+@*>/

8 >@.*.98 >@.*.9

Balance

after 7 year

Balance

after 7 year Balance

after 1 years

Balance

after 1 years*

A i i 14 24


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14 - 24

7his completes Chapter 14

3. Ammortization of Loan

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