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Simple Interest

Debtor/Makeran individual or institution that borrows money

for any purpose

Lender

an individual or institution who loans the money

InterestIpayment for the use of borrowed money or the

amount earned on an invested money

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Definition of Terms (continued)

PrincipalP

the capital or sum of money borrowed orinvested

Rate o f In terestr

fractional part of the principal that is paid on theloan or investment (expressed as percent) and theannual rate set by the lender

Timet

number of years for which the money isborrowed or invested

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Definition of Terms (continued)

Final Amount o r Matur i ty ValueFcombined amount of the principal and the

interest accumulated over a certain period of time

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Simple Interest

interest computed based on the principal and ispaid at the end of the specified period of time

Formula:

I= Prt

where

= principal investedP= rate of interest in decimalsr

= time in yearst

r t

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Find the Principal, Rate or Time Using the

Simple Interest Formula

P r t

I

P r t

I

P r t

I

P r t

I

I Pr t

IP

r t

Ir

Pt

It

Pr

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Examples

1. Find the interest paid by Ms. April on Php25,000

that she borrowed for three years at 4% simple

interest.

2. Determine the simple interest to be paid by Lornaif she borrowed Php1,200 at 6 % for 8 months.

3. At what rate of interest did Mary invest the

amount of Php27,500 for it to earn a simple interest

of Php3, 245 for three years?

Final Amount or Maturity Value F

SIMPLE INTEREST

F P I F P Pr t P rt 1

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Examples (continued)

4. How much was borrowed by Ms. Michelle if the

interest she paid after 3 months at 10.5% simple

interest is Php3,000?

5. How long should Dan invest the amount of

Php80,000 to earn an interest of Php4,500 at 6.5%

simple interest?

6. How much is the final amount would Ms. Nessy

receive if she invested Php75,000 for 4 years at 5

% simple interest?

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Ordinary and Exact Interest

Ordinary Interest vs. Exact Interesti

O iE

Default : Ord inary Interest

iO - a rate per day that assumes 360 days

per year

iE - a rate per day that assumes 365 days

per year

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Examples

1. For 209 days, what would be the interest if Gretel

invested Php43,500 at

(a) 5 % ordinary simple interest?

(b) 5 % exact simple interest?

(c) How much is the difference between these twoinvestments?

2. Use ordinary interest to find the final amount due on

Php 75,150 for 420 days at 12.75%

3. Use exact interest to find the interest and final

amount due on Php25,345 for 636 days at 10.25%

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Ordinary and Exact Interest

Why do you think banks prefer to use

ordinary interest in their business? Supportyour answer.

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Actual and Approximate Time

Default : Actual Time

Actual time based on counting the exact

number of days in a time period

Approximate time based on counting 30

days in each month

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ACTUAL NUMBER OF DAYS PER MONTH

MONTH NUMBER OF DAYS

January 31 days

February28 days, 29 in leap

years

March 31 days

April 30 days

May 31 days

June 30 days

July 31 days

August 31 daysSeptember 30 days

October 31 days

November 30 days

December 31 days

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Examples

The approximatetime from July 12 toSeptember 12 is60 days.

To find the actualtime from July 12 toSeptember 12, add the following:

Days in July (31 - 12 ) 19

Days in August 31

Days in September +1262 days

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Interest Between Dates

actual time=i actO Pr 360

approximate time=i appO Pr 360

actual time

=i act

E Pr 365

approximate time=i appE Pr 365

Default

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Examples

1. Using the four methods, find the interest onPhp23,250 at 5 2/3% simple interest from August 9,

2003 to May 18, 2004. (p. 20)

2. Determine the ordinary interest on Php53,000 at11% from June 17, 2003 to October 9, 2003 using

actual and approximate time. (p. 19)

3. What amount should be paid on February 10, 2004

for a loan of Php16,020 made on October 7, 2003 with

4 3/5% simple interest? (p. 21)

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Do it on your own

What final amount should

Carol pay for a loan of

Php8,200 at 14 % simple

interest she borrowed inMarch 10, 2000 if she

promised to pay on

November 25, 2000?

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Present Value

amount of loan or investment known as theprevailing value of an amount scheduled at some

future time

also called principal and denoted by P

formula is given by

where

FP

r t 1

= accumulated amountF= simple interest rate in decimalsr

= term of loan or investmentt

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Examples1. How much must Ivy invest today in order to havePhp32,500 available in 4 years if money is worth 12% simple

interest?

2. Find the present value of Php19,200 for 120 days at 4 5/8% simple interest.

3. Determine the present value of a 7-month 12.3% simple

interest loan if its final amount is Php19, 345?

4. Find the present value ofDorys loan, which amounted to

Php45,650.75 from January 5, 2008 to April 25, 2008 if the

money is worth 8.5% simple interest.

PRESENT VALUE