Simple Interest Discount

7/23/2019 Simple Interest Discount

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SIMPLE INTEREST ANDSIMPLE DISCOUNT

Concepts: Simple Interest, Simple Discount,Ordinary and Exact Simple Interest, Interest onActual and Approximate Time, Promissory Note



OBJECTIVES:

At the end of this unit, you must e ale to

!" differentiate simple interest from simplediscount#

$" compute simple interest usin% actual or

approximate time#&" compute ordinary and exact interest#

'" determine (hether the promissory note is aninterest earin% or a non)interest)earin% note#

*" sol+e prolems on simple interest and simple

discount usin% appropriate formulas"

Simple Interest and Simple Disc!nt



OVERVIE"

or e+ery amount orro(ed or in+ested acorrespondin% portion of the amount is paid orearned and this is called interest"

Simple interest is an interest that ispaid-earned at the end of a loan-in+estmentperiod"



OVERVIE" #CONTINUED$%

.hen interest is paid in ad+ance, interest deducted

from the principal is called simple discount"

.hen a orro(er is not ready to pay his det, he can

(rite a note stipulatin% his promise to pay an amount aa specified time (ith a specified interest rate"



DE&INITION O& TERMS

Debtor/Maker

an indi+idual or institution that orro(s money for any

purpose

Lender

an indi+idual or institution (ho loans the money

Interest I

payment for the use of orro(ed money or the amount

earned on an in+ested money



DE&INITION O& TERMS #CONTINUED$%

Principal P

the capital or sum of money orro(ed or in+ested

Rate of Interest r

fractional part of the principal that is paid on the loan or

in+estment /expressed as percent0

Time t

numer of years for (hich the money is orro(ed or

in+ested



DE&INITION O& TERMS #CONTINUED$%

Maturity Value or Final Amount F

comined amount of the principal and the interest

accumulated o+er a certain period of time

/also called Future Value)



SIMPLE INTEREST

interest computed ased on the principal and is paid at the

end of the specified period of time

ormula:

(here

I Pr t

= principal invested P

= rate of interest in decimalsr

= time in yearst



E'AMPLES!" ind the interest paid y 1s" April on

P$*,222 that she orro(ed for three years at

'3 simple interest"$" Determine the simple interest to e paid y

4orna if she orro(ed P!,$22 at 5 63 for 7

months8

&" At (hat rate of interest did 1ary in+est the

amount of P$9,*22 for it to earn a simpleinterest of P&, $'* for three years8

inal Amount or 1aturity alue F

SIMPLE INTEREST

F P I

F P Pr t P rt =

1



E'AMPLES #CONTINUED$%

'" ;o( much (as orro(ed y 1s" 1ichelle if the interest

she paid after & months at !2"*3 simple interest is P&,2228

*" ;o( lon% should Dan in+est the amount of P72,222 toearn an interest of P',*22 at 5"*3 simple interest8

5" ;o( much is the final amount (ould 1s" Nessa recei+e ifshe in+ested P9*,222 for ' years at * < 3 simple interest8



ORDINAR( AND E'ACT INTEREST

Ordinary Interest, +s" Exact Interest,

Default !rdinary Interest

) a rate per day that assumes &52 daysper year

) a rate per day that assumes &5* daysper year

i O i

E

i O

i E



ORDINAR( AND E'ACT INTEREST

.hy do you thin= an=s prefer to useordinary interest in their usiness8 Supportyour ans(er"



ACTUAL AND APPRO'IMATE TIME

Default Actual Time

Actual time > ased on countin% the exactnumer of days in a time period

Approximate time > ased on countin% &2 days

in each month



ACTUAL NUMBER O& DA(S PER MONT)

1ONT; N?1@E O DABS

anuary &! dayseruary

$7 days, $ in leapyears

1arch &! days

April &2 days

1ay &! days

une &2 days

uly &! days

Au%ust &! days

Septemer &2 days

Octoer &! days

No+emer &2 days

Decemer &! days



E'AMPLES

The appr*imate time from uly !$ toSeptemer !$ is +, days"

To find the act!al time from uly !$ toSeptemer !$, add the follo(in%:

Days in uly /&! ) !$ 0 !

Days in Au%ust &!

Days in Septemer F!$ +- da.s



INTEREST BET"EEN DATES

Default

actual time=

i act O Pr

÷

360

approximate time=i appO Pr

÷

360

actual time=i act E Pr

÷

365

approximate time=i app E Pr

÷

365



INTEREST BET"EEN DATES

"oteI/ t0e t.pe / interest is nt speci/iedin an. pr1lem2 t0e pr1lem 3ill 1esl4ed !sin5 t0e #anker$s Rule orordinary interest in actual time%



E'AMPLES

9" or $2 days, (hat (ould e the interest if

Gretel in+ested Php '& *22"22 at

/a0 * 63 ordinary simple interest8/0 * 63 exact simple interest8

/c0 ;o( much is the difference et(een these

t(o in+estments8

7" Determine the the ordinary and exactinterest on P7&*2 at !93 from eruary !'$2!2 to Septemer !$ of the same year usin%actual and approximate time"



DO IT ON (OUR O"N

!" .hat final amount should Carol

pay for a loan of P7,$22 at !' < 3

simple interest she orro(ed on1arch !2, $222 if she promised to

pay on No+emer $*, $222"

$" On Au%ust 5, Gay (ent to the 1SS @an= and too=out a loan for 72,222, at !23 interest, for 52₱

days"a" .hat is the maturity +alue of the loan8" .hen (ill the loan mature8

ANS: P62,7896-

ANS: P28

ANS: T0e lan 3ill mat!re n Oct9 ;9



PRESENT VALUE amount of loan or in+estment =no(n as the pre+ailin%

+alue of an amount scheduled at some future time also called principal and denoted y P

formula is %i+en y

(here

F

P rt =

1

= accumulated amountF

= simple interest rate in decimalsr

= term of loan or investmentt



E'AMPLES

!2" ;o( much must I+y in+est today in order to ha+e

P&$,*22 a+ailale in ' years if money is (orth !$3 simpleinterest

!!" ind the present +alue of P!,$22 for !$2 days at ' *-73 simple interest"

!$" Determine the present +alue of a 9)month !$"&3 simpleinterest loan if its final amount is P!, &'*8

PRESENT VALUE



E'AMPLES

!&" ind the present +alue of DoryHs loan, (hich amounted

to P'*,5*2"9* from anuary *, $227 to April $*, $227 if themoney is (orth 7"*3 simple interest"

PRESENT VALUE



SIMPLE DISCOUNT interest is computed ased on the final

amount and is paid at the e%innin% of aspecified period of time

interest paid in advanced

formula is %i+en y

(here a

I Fdt

= amount of loanF

= simple discount rate in decimalsd

= term of discountt

SIMPLE DISCOUNT



SIMPLE DISCOUNT

Amount of loan is eual to the maturity

+alue of the loan"

4et proceeds P e the amount recei+ed

y the orro(er after remo+in% the

interest on the loan

To sol+e for the proceeds, (e use the formula

a P F I

P F dt 1



SIMPLE DISCOUNT

To discount loan for t years means to findthe present +alue /proceeds0 P of on aday (hich is t years efore is due"

the interest on the present value P

the discount on the loan F I



Basic terms !sed 3it0 simpleinterest

Simple interest rate for P$222"@orro(er recei+es the amount P$222

Interest is P!$*"

@orro(er mustpay ac= P$!$*on thematurity dateof the loan"

Maturity Value



Basic terms !sed 3it0 simpledisc!nt ntes

Simple discount rate for P$222"

Amount of loan P$222@orro(er recei+es P!79*"

Interest is P!$*"

@orro(er must

pay ac= P$222on the maturitydate of the loan"

Proceeds

Discount

Maturity Value



E'AMPLES

!'" Geor%e orro(ed P!52,222 from the D4S? Credit

Cooperati+e for a term of one year and & months" Theinterest char%ed is !23 simple discount rate" ind the

proceeds of the loan"

!*" 1s" Jamora needs P!7,722 today" ;o( much should she

orro( from 1sD an= char%in% !5 K3 interest)in)ad+ancepayale in $ years8

!5" ;o( lon% should P$*,222 e discounted to ha+e proceed

of P$$,222 at !'3 simple discount rate8

SIMPLE DISCOUNT



E'AMPLES!9" Determine the discount rate if P$*,222 is the proceeds o

a loan of P&*,222 due in !' months8

!7" At a simple discount rate of !$3, find the discount onP5,**2 orro(ed on anuary !&, $22 if the det is repaid ouly !&, $22"

To discount an amount is t&e same as findin' t&e presen(alue )proceeds* of an amount at a 'i(en simple discountrate%

!7" Discount P!7,222 from Au%ust &, $2!2 to 1ay ', $2!! (it

a simple discount rate of 5"$3"

SIMPLE DISCOUNT

E*ercises



!" Sam is sa+in% up to uy the ne( PlayStation that (ill ereleased in $ years" It is expected to cost P&*,222" ;o( mudoes Sam need to deposit in a sa+in%s account today that is

earnin% 5"'*3 per annum for him to ha+e enou%h money inorder to purchase the PlayStation in $ years8

E*ercises

$" Sam has P52,222 and canHt decide (hich of thefollo(in% $ offers are etter" @an= A@C 4td is currently

offerin% customers 5"*23 simple interest for 9 monthsand an= LBJ 4td is offerin% 5"*3 simple interest for 'months" .hich an= should Sam an= at8

&" Discount P!7,222 from Au%ust &, $2!2 to 1ay ', $2!!(ith a simple discount rate of 5"$3"



Cmparin5 Interest Rates

imple Interest Notes vs imple Discount Not

.hich loan Mcosts more to the orro(er8

Simple interest nteP&,222 93 for !2 months"

Simple disc!nt ntP&,222 93 for !2 mon

I < PrtI &222 x "29 x !2-!$I P=;

I < &dtI &222 x "29 x !2-!I P=;

@orro(er %etsQQQQQQQQQQ"

@orro(er %etsQQQQQQQQQQ"&222 $7$*

Simple Interest Discount

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