8.1 Simple 8.1 Simple InterestInterest

Key Terms

Principal: A sum of money that is Principal: A sum of money that is borrowed or invested.borrowed or invested.

Simple interest: Interest earned or paid only on Simple interest: Interest earned or paid only on the the original sum of money that was original sum of money that was

invested or borrowed.invested or borrowed. Interest: The money earned from an investment Interest: The money earned from an investment

or or the cost of borrowing money.the cost of borrowing money. Amount: The total value of an investment or loan. Amount: The total value of an investment or loan.

The amount is given by A=P+I, where The amount is given by A=P+I, where A is A is the amount, P is the principal, and I is the amount, P is the principal, and I is

the interest.the interest.

Easy Memory TrickEasy Memory Trick

PrincipalPrincipal

Is the sum of money that is borrowed Is the sum of money that is borrowed or investedor invested

Example #1Example #1

Kenny wants to invest Kenny wants to invest $2000. Her bank will $2000. Her bank will pay 6% of the pay 6% of the principal principal each year each year the money is kept in a the money is kept in a savings account that savings account that earns earns simple interestsimple interest..

Calculate the interest Calculate the interest earned and the amount of earned and the amount of the investment at the end the investment at the end of each year for three of each year for three years. Record results in a years. Record results in a table.table.

YEARYEAR INTERESINTEREST T EARNEDEARNED

AMOUNTAMOUNT

00 ________ $2000$2000

11

22

33

How to SolveHow to Solve 1ST YEAR: Given that P = $2000 Rate = 6% or 0.06 I = R x P I = 0.06 x $2000 I = $120 $120 + $2000 = $2120

YEARYEAR INTEREST INTEREST EARNEDEARNED

($)($)

AMOUNTAMOUNT

($)($)

00 ________ 20002000

11 120120 21202120

22 120120 22402240

33 120120 23602360

InterestInterest

Simple interest: Interest earned or Simple interest: Interest earned or paid only on the original sum of paid only on the original sum of money that was invested or money that was invested or borrowed.borrowed.

Example #2Example #2

Vivian invests $3240 at a simple Vivian invests $3240 at a simple interest rate of 2.4% per year. interest rate of 2.4% per year.

a)a)Calculate the interest earned each Calculate the interest earned each year. year.

b)b)Calculate the amount and the total Calculate the amount and the total interest earned after 20 years.interest earned after 20 years.

How to SolveHow to Solvea)a) Given: Given:

Principal = $3240Principal = $3240

Rate = 2.4% = 0.024Rate = 2.4% = 0.024

Time = 1 yearTime = 1 year

Interest = PRTInterest = PRT

I = 3240 x 0.024 x 1I = 3240 x 0.024 x 1

= $77.76= $77.76

The total interest of an investment of The total interest of an investment of $3240 for 1 year at a simple interest rate of $3240 for 1 year at a simple interest rate of 2.4% is $77.76. 2.4% is $77.76.

Continuation of example 2…Continuation of example 2…b)b) Given: Given:

Principal = $3240Principal = $3240

Rate = 2.4% = 0.024Rate = 2.4% = 0.024

Time = 20 yearsTime = 20 years

I= PRTI= PRT

=3240(0.024)(20)=3240(0.024)(20)

= 1555.20= 1555.20

Amount = P + IA = 3240 +1555.2 = 4795.20

Continuation for part b)Continuation for part b)

Total Interest = Amount – PrincipalTotal Interest = Amount – Principal

TTI I = 4795.20 – 3240 = $1555.20= 4795.20 – 3240 = $1555.20

After 20 years, Vivian will have After 20 years, Vivian will have $4795.20 and will have earned $4795.20 and will have earned $1555.20 in interest. $1555.20 in interest.

RateRate

usually given as a percentageusually given as a percentage Expressed as a decimal when Expressed as a decimal when

calculating the simple interest using calculating the simple interest using the formula I= PRTthe formula I= PRT

Sometimes seen as __ %/a, which Sometimes seen as __ %/a, which means __% per annum, or yearmeans __% per annum, or year

To find rate, rearrange formulaTo find rate, rearrange formula

I= PRT ( R= I / PT)I= PRT ( R= I / PT)

Example #3Example #3

Gobin has a balance of $2845 on her Gobin has a balance of $2845 on her credit card. What rate of simple credit card. What rate of simple interest is she being charged if she interest is she being charged if she must pay $26.19 interest for the 12 must pay $26.19 interest for the 12 days her payment is late?days her payment is late?

How to SolveHow to Solve

Given: Given:

Interest= 26.19Interest= 26.19

Principal= 2845Principal= 2845 the rate of the rate of Time= 12/365Time= 12/365 simple interest is simple interest is

28%/a.28%/a. Rate= I/ PTRate= I/ PT

Rate= 26.19/ 2845 x 12/365Rate= 26.19/ 2845 x 12/365

= 0.28= 0.28

0.28 x 100= 28%/a0.28 x 100= 28%/a

TimeTime

The length of the periodThe length of the period A key element to calculating interestA key element to calculating interest For simple interest it’s usually For simple interest it’s usually

annuallyannually

Example #4Example #4

Sinthura invests $4850 at a simple Sinthura invests $4850 at a simple interest rate of 7.6% per year. If she interest rate of 7.6% per year. If she wants the money to increase to wants the money to increase to $8000, how long will she need to $8000, how long will she need to invest her money?invest her money?

How to SolveHow to SolveGiven:Given:

P = $4850P = $4850

R = 7.6% = 0.076R = 7.6% = 0.076

A = $8000A = $8000

Formula: A = P + PRTFormula: A = P + PRT

8000 = 4850 + (4850) (0.076) x T8000 = 4850 + (4850) (0.076) x T

8000 = 4850 + 368.6 x T8000 = 4850 + 368.6 x T

3150 = 368.6 x T3150 = 368.6 x T

T = 8.546 T = 8.546

Continuation…Continuation…

Since it is over 8 years, we have to Since it is over 8 years, we have to calculate the number of days 0.546 calculate the number of days 0.546 years is.years is.

8.546 – 8 = 0.5468.546 – 8 = 0.546

0.546 x 365 days = 199.2 days 0.546 x 365 days = 199.2 days

Sinthura would have to invest her Sinthura would have to invest her money for 8 years and 200 days to get money for 8 years and 200 days to get $8000. $8000.

Example #5Example #5Calculate the total amount earned at the end of Calculate the total amount earned at the end of

each period: 1each period: 1st,st, 2 2ndnd, 3, 3rdrd, and 15, and 15th.th. $500 at 9%/a simple interest rate$500 at 9%/a simple interest rate

AA1 1 = P + PRT= P + PRT

= 500 + (500) (0.09) (1)= 500 + (500) (0.09) (1)

= 500 + 45= 500 + 45

= $545= $545

The total amount of an investment of $500 The total amount of an investment of $500 for 1 year at 9%/a simple interest is $545, and for 1 year at 9%/a simple interest is $545, and the total interest earned is $45. the total interest earned is $45.

AA22 = 500 + (500) (0.09) (2)= 500 + (500) (0.09) (2)

= 500+ 90 = 500+ 90

= $590= $590

The total amount of an investment of $500 The total amount of an investment of $500 for 2 years at 9%/a simple interest is $590, and for 2 years at 9%/a simple interest is $590, and the total interest earned is $90. the total interest earned is $90.

AA3 3 = 500 + (500) (0.09) (3)= 500 + (500) (0.09) (3)

= 500 + 135= 500 + 135

= $635 = $635

The total amount of an investment The total amount of an investment of $500 for 3 years at 9%/a simple of $500 for 3 years at 9%/a simple interest is $635, and the total interest interest is $635, and the total interest earned is $135. earned is $135.

AA15 15 = 500 + (500) (0.09) (15)= 500 + (500) (0.09) (15)

= 500 + 675= 500 + 675

= $1175 = $1175

The total amount of an investment The total amount of an investment of $500 for 15 years at 9%/a simple of $500 for 15 years at 9%/a simple interest is $1175, and the total interest interest is $1175, and the total interest earned is $675. earned is $675.

Key ideasKey ideas

Simple interest is calculated only on Simple interest is calculated only on the principalthe principal

(total amount) T(total amount) Taa and (total interest) and (total interest) TTII, are linear functions ,their graphs , are linear functions ,their graphs are straight linesare straight lines

Need to KnowNeed to Know

To calculate simple interestTo calculate simple interest

I= PRT I= PRT

I= interestI= interest

P= principalP= principal

R= interest rate ( in decimal)R= interest rate ( in decimal)

T= time( expressed in the same period T= time( expressed in the same period as the interest rate, usually per year)as the interest rate, usually per year)

Total amount of money earned from Total amount of money earned from an investment and the simple an investment and the simple interest can be determined by this interest can be determined by this formulaformula

TTaa= P+ PRT= P+ PRT

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