8.1 Simple Interest

Key Terms Principal: A sum of money that is borrowed or invested. Principal: A sum of money that is borrowed or invested. Simple interest: Interest earned or paid only on the original sum of money that was invested or borrowed. Simple interest: Interest earned or paid only on the original sum of money that was invested or borrowed. Interest: The money earned from an investment or the cost of borrowing money. Interest: The money earned from an investment or the cost of borrowing money. Amount: The total value of an investment or loan. The amount is given by A=P+I, where A is the amount, P is the principal, and I is the interest. Amount: The total value of an investment or loan. The amount is given by A=P+I, where A is the amount, P is the principal, and I is the interest.

Easy Memory Trick I P R T

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

Example #1 Kenny wants to invest $2000. Her bank will pay 6% of the principal each year the money is kept in a savings account that earns simple interest. Kenny wants to invest $2000. Her bank will pay 6% of the principal each year the money is kept in a savings account that earns simple interest. Calculate the interest earned and the amount of the investment at the end of each year for three years. Record results in a table. Calculate the interest earned and the amount of the investment at the end of each year for three years. Record results in a table. YEAR INTEREST EARNED AMOUNT 0 ____ ____$

How 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

YEAR INTEREST EARNED ($)AMOUNT($) 0 ____ ____

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

Example #2 Vivian invests $3240 at a simple interest rate of 2.4% per year. Vivian invests $3240 at a simple interest rate of 2.4% per year. a) Calculate the interest earned each year. b) Calculate the amount and the total interest earned after 20 years.

How to Solve a)Given: Principal = $3240 Rate = 2.4% = Time = 1 year Interest = PRT I = 3240 x x 1 = $77.76 = $77.76 The total interest of an investment of $3240 for 1 year at a simple interest rate of 2.4% is $ The total interest of an investment of $3240 for 1 year at a simple interest rate of 2.4% is $77.76.

Continuation of example 2… b)Given: Principal = $3240 Rate = 2.4% = Time = 20 years I= PRT =3240(0.024)(20) =3240(0.024)(20) = = Amount = P + I A = =

Continuation for part b) Total Interest = Amount – Principal T I = – 3240 = $ After 20 years, Vivian will have $ and will have earned $ in interest. After 20 years, Vivian will have $ and will have earned $ in interest.

Rate usually given as a percentage usually given as a percentage Expressed as a decimal when calculating the simple interest using the formula I= PRT Expressed as a decimal when calculating the simple interest using the formula I= PRT Sometimes seen as __ %/a, which means __% per annum, or year Sometimes seen as __ %/a, which means __% per annum, or year To find rate, rearrange formula To find rate, rearrange formula  I= PRT ( R= I / PT)

Example #3 Gobin has a balance of $2845 on her credit card. What rate of simple interest is she being charged if she must pay $26.19 interest for the 12 days her payment is late? Gobin has a balance of $2845 on her credit card. What rate of simple interest is she being charged if she must pay $26.19 interest for the 12 days her payment is late?

How to Solve Given: Given: Interest= Interest= Principal= 2845the rate of Time= 12/365simple interest is 28%/a. Rate= I/ PT Principal= 2845the rate of Time= 12/365simple interest is 28%/a. Rate= I/ PT Rate= 26.19/ 2845 x 12/365 Rate= 26.19/ 2845 x 12/365 = 0.28 = x 100= 28%/a 0.28 x 100= 28%/a

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

Example #4 Sinthura invests $4850 at a simple interest rate of 7.6% per year. If she wants the money to increase to $8000, how long will she need to invest her money?

How to Solve Given: P = $4850 R = 7.6% = A = $8000 Formula: A = P + PRT 8000 = (4850) (0.076) x T 8000 = x T 3150 = x T T = 8.546

Continuation… Since it is over 8 years, we have to calculate the number of days years is – 8 = x 365 days = days Sinthura would have to invest her money for 8 years and 200 days to get $8000. Sinthura would have to invest her money for 8 years and 200 days to get $8000.

Example #5 Calculate the total amount earned at the end of each period: 1 st, 2 nd, 3 rd, and 15 th. $500 at 9%/a simple interest rate $500 at 9%/a simple interest rate A 1 = P + PRT = (500) (0.09) (1) = (500) (0.09) (1) = = = $545 = $545 The total amount of an investment of $500 for 1 year at 9%/a simple interest is $545, and the total interest earned is $45. The total amount of an investment of $500 for 1 year at 9%/a simple interest is $545, and the total interest earned is $45.

A 2 = (500) (0.09) (2) = = = $590 = $590 The total amount of an investment of $500 for 2 years at 9%/a simple interest is $590, and the total interest earned is $90. The total amount of an investment of $500 for 2 years at 9%/a simple interest is $590, and the total interest earned is $90. A 3 = (500) (0.09) (3) = = = $635 = $635

The total amount of an investment of $500 for 3 years at 9%/a simple interest is $635, and the total interest earned is $135. The total amount of an investment of $500 for 3 years at 9%/a simple interest is $635, and the total interest earned is $135. A 15 = (500) (0.09) (15) = = = $1175 = $1175 The total amount of an investment of $500 for 15 years at 9%/a simple interest is $1175, and the total interest earned is $675.

Key ideas Simple interest is calculated only on the principal Simple interest is calculated only on the principal (total amount) T a and (total interest) T I, are linear functions,their graphs are straight lines (total amount) T a and (total interest) T I, are linear functions,their graphs are straight lines

Need to Know To calculate simple interest To calculate simple interest  I= PRT  I= PRT I= interest P= principal R= interest rate ( in decimal) T= time( expressed in the same period as the interest rate, usually per year)

Total amount of money earned from an investment and the simple interest can be determined by this formula Total amount of money earned from an investment and the simple interest can be determined by this formula  T a = P+ PRT

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