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8.1 Simple Interest

8.1 Simple Interest. Key Terms. 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. Interest: The money earned from an investment or the cost of borrowing money.

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8.1 Simple Interest

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  1. 8.1 Simple Interest

  2. Key Terms • 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. • 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.

  3. Easy Memory Trick

  4. Principal • Is the sum of money that is borrowed or invested

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

  6. 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

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

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

  9. How to Solve a) Given: Principal = $3240 Rate = 2.4% = 0.024 Time = 1 year Interest = PRT I = 3240 x 0.024 x 1 = $77.76 The total interest of an investment of $3240 for 1 year at a simple interest rate of 2.4% is $77.76.

  10. Continuation of example 2… Amount = P + I A = 3240 +1555.2 = 4795.20 b) Given: Principal = $3240 Rate = 2.4% = 0.024 Time = 20 years I= PRT =3240(0.024)(20) = 1555.20

  11. Continuation for part b) Total Interest = Amount – Principal TI = 4795.20 – 3240 = $1555.20 After 20 years, Vivian will have $4795.20 and will have earned $1555.20 in interest.

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

  13. 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?

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

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

  16. 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?

  17. How to Solve Given: P = $4850 R = 7.6% = 0.076 A = $8000 Formula: A = P + PRT 8000 = 4850 + (4850) (0.076) x T 8000 = 4850 + 368.6 x T 3150 = 368.6 x T T = 8.546

  18. Continuation… Since it is over 8 years, we have to calculate the number of days 0.546 years is. 8.546 – 8 = 0.546 0.546 x 365 days = 199.2 days Sinthura would have to invest her money for 8 years and 200 days to get $8000.

  19. Example #5 Calculate the total amount earned at the end of each period: 1st, 2nd, 3rd, and 15th. • $500 at 9%/a simple interest rate A1 = P + PRT = 500 + (500) (0.09) (1) = 500 + 45 = $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.

  20. A2= 500 + (500) (0.09) (2) = 500+ 90 = $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. A3 = 500 + (500) (0.09) (3) = 500 + 135 = $635

  21. 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. A15 = 500 + (500) (0.09) (15) = 500 + 675 = $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.

  22. Key ideas • Simple interest is calculated only on the principal • (total amount) Ta and (total interest) TI, are linear functions ,their graphs are straight lines

  23. Need to Know • To calculate simple interest  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)

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

  25. Review your worksheets in preparation for your up-coming Quiz

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