Chapter 5 - Annuities

7/21/2019 Chapter 5 - Annuities

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CHAPTER 5:

ANNUITIES



Capital Budgeting

• Capital budgeting is a process used bycompanies for evaluatinginvestments/expenditures.

• Capital budgeting usually involves thecalculation of each project's future byconsidering “time value of money”.



Time Value of Money

• F ! " #$%r&n

• " ! F

#$%r&n

F ! Future alue

" ! "resent alue

r! (ate of interestn ! term in years



Eample

)hat is the balance in an account at the end of$* years if +,-** is deposited today and theaccount earns 0 interest compoundedannually1

F ! " #$%r&n

! +,-** #$%*.*&$*

! +2-3**.4$



Eample

5o6 much 7 have to deposit in an account todaythat pays $,0 interest- compounded annually-so that 7 have a balance of +,*-*** in theaccount at the end of $* years.

" ! F

#$%r&n

" ! +,*-***

#$%*.$,&$* ! +4-28.4



Annuity

• 9nnuity is a series of #usually& e:ualpayments made at #usually& e:ual intervals of

time. ;< of annuity=

•>hop rentals

•7nsurance policy premium

•regular deposits to saving accounts

•installment payments



Cla!!e! of Annuity

Fa#normal& ! "?

"ayment made end of the year/month

"? ! "eriodic payment

9! 9mount- after value

r ! rate of interestt! time in years

n! no of interest converted in years

#$%r/n&nt @ $ r/n



Cla!!e! of Annuity

Fa#due& ! "? x #$%r&

"ayment made beginning of the year/month

"? ! "eriodic payment

9! 9mount- after value

r ! rate of interestt! time in years

n! no of interest converted in years

#$%r/n&nt @ $ r/n



Eample

7nvestment 6as set up and :uarterly paymentsof +$-** have to be made for 4 years at theend of each month. 7f annual interest rate is$40- 6hat is the value of investment after 4years.



Sin"ing #und

7f a person 6ants to purchaseasset/ordinary annuity to guarantee

certain amount of money in future- personcan determine the amount of payment byusing sinAing fund payment method



Sin"ing #und #o$mula

>F! F x r

B #$%r&n @ $

>FD >inAing Fund "ayment

FD Future alue

rD period of interest ratenD Eumber of periods



Eample

eannette- o6ner of eanetteGs 5ealthClub- 6ants to purchase ne6 pecDdecAmachine in 2 years. Hhe cost of machine

is +8**. Find the sinAing fund method ifthe interest rate is $*0 annually.



>F! F x r

B #$%r&n @ $

FD +8**rD $*0x$ - *.$ x $

nD 2x$

+8**x*.$/##$%*.$*&2D$& ! +,3$.8*



Amo$ti%ation

Hhe process of paying off a loan #plusinterest& by maAing a series of regular-e:ual payments is called amortiIation-

and such a loan is called an amortiIedloan.



Amo$ti%ation

Hable value for 7nterest factor for mortgage

&ea$! '( )( *( +,(

$* $$.4$ $,.$ $,.43 $2.,,

,* 3.3 J.23 8.** 8.44

2* 4.4 3.2 J.* J.3J





Amo$ti%ation S./edule Step!

$. Find the interest #7&

7 ! "rt

"! "rincipal

r! (ate of interest

t! Herm in months




,. Find amount paid to the principal #?onthly"ayment #?"& @ 7nterest #7&&

?"! "rinciple x table value $***




2. Find balance of principle by subtract amountobtained in >tep ,.

Kalance of "rincipal! "rincipal @ 9mount "aidto principle

(epeat the step 6ith latest principal to get ne6

interest-amount paid L ne6 balance



Eample

$. 9 person purchased a home 6ith +J*-***loan at J0 for ,* years. ?aAe amortiIationtable for 2 months.

Find amortiIation for month $

7 ! "rt

! +J*-***x*.*Jx$/$,

! +22.22



Eample

?onthly payment

?"! J*-*** x J.,3

$-*** ! 448.4

9mount paid to principal

?"D7448.4D 22.22

! $24.,3



Eample

Kalance of principle #"rinciple @ 9mt paid toprinciple&

J*-***D$24.,3 ! 38-J42.32

?onth ,

7!"rt ! 38-J42.32 x *.*J x $/$,

! 2,., MMM continue step , and 2



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Chapter 5 - Annuities