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LESSON 2 – COMPOUND INTEREST

LESSON 2 – COMPOUND INTEREST . WARM-UP : Write the general formula that represents exponential growth. 2. Sazia invests $800 at 6% interest compounded annually. a) Determine the interest she earns after 1 year. b) Determine the accumulated amount after 1 year.

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LESSON 2 – COMPOUND INTEREST

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  1. LESSON 2 – COMPOUND INTEREST WARM-UP: Write the general formula that represents exponential growth. 2. Saziainvests $800 at 6% interest compounded annually. a) Determine the interest she earns after 1 year. b) Determine the accumulated amount after 1 year. c) Determine the accumulated amount after 2 years.

  2. Compound Interest • COMPOUND INTEREST • Interest is earned on the principal AND any previously accumulated interest. •  You are earning interest on interest. • For compound interest, the number of times interest is compounded in a year can vary • Annually • Semi-Annually • Quarterly • Monthly • Weekly • Bi-Weekly • Daily

  3. Activity 1 – Investigating Compound Interest • Shaheer invests $600 earning 7% per annum compounded annually. • Complete the chart below to determine how much money he has at the end of each year for 5 years.

  4. Activity 1 – Investigating Compound Interest Shaheer invests $600 earning 7% per annum compounded annually. b) Graph the data on the grid below.

  5. Activity 1 – Investigating Compound Interest • Shaheer invests $600 earning 7% per annum compounded annually. • c) What kind of function does the data model? • d) Write the equation of the function that models this data.

  6. Activity 1 – Investigating Compound Interest • Shaheer invests $600 earning 7% per annum compounded annually. • e) Consider the accumulated amounts in the chart: 642, 686.94, 735.03, 786.48, 841.53What kind of sequence is modeled? How do you know? • f) Write the general term formula for this sequence.

  7. Activity 1 – Investigating Compound Interest • Shaheer invests $600 earning 7% per annum compounded annually. • g) What does the 600 represent in both of the equations you found in parts (d) and (f)? • h) What does the common ratio/base (1.07) represent?

  8. Activity 1 – Investigating Compound Interest • Shaheer invests $600 earning 7% per annum compounded annually. • i) Determine a general formula for the accumulated amount on an investment where interest is calculated at the end of each year for t years. • j) Determine a general formula for the interest on an investment where interest is compounded annually (calculated at the end of each year) for t years.

  9. Activity 2 – Investigating Compound Interest • Shaheer invests $600 earning 7% per annum compounded semi-annually. • Complete the chart below to determine how much money he has at the end of each 6 month compounding period for 2 years. This means he earns 3.5%in interest every 6 months.

  10. Activity 2 – Investigating Compound Interest Shaheer invests $600 earning 7% per annum compounded semi-annually. b) How will the equation A = P (1 + r)t need to be modified to accommodate multiple interest earning periods in a year? This means he earns 3.5%in interest every 6 months.

  11. Summary • Compound Interest Formula: where Ais the accumulated amount Pis the principal amount iis the interest rate per compounding period (as a decimal) nis the number of compounding periods.

  12. Compound Interest EXAMPLE 1:How many times a year is interest compounded…

  13. Compound Interest • EXAMPLE 2:The rate of interest for an investment is 5% per annum. What is the interest rate for each compounding period? • annually b) semi-annually • c) monthly d) bi-weekly

  14. Compound Interest • EXAMPLE 3:How many compounding periods are there for each of the following loans? • Compounded monthly for 3 years • Compounded annually for 5 years • Compounded weekly for 2 years

  15. Compound Interest • EXAMPLE 4:Determine the accumulated amount if $2300 is invested for 4 years at 6% per year compounded… • annually • semi-annually

  16. Compound Interest • EXAMPLE 4:Determine the accumulated amount if $2300 is invested for 4 years at 6% per year compounded… • c) quarterly • d) monthly • (Cont’d) • Which earns more? Compounding Annually, Semi-Annually, Quarterly or Monthly?

  17. Comparison of Interests Simple Interest Compound Interest • Interest on PRINCIPAL only • Interest on principal AND accumulated interest • Formulas: • Formulas: • Compounded annually • Compounding period may vary • (semi-annually, weekly, etc.)

  18. Compound Interest EXAMPLE 5:Lajanthanwants to have a total investment of $8000 in 6 years, with interest compounded semi-annually at 7% per annum. How much does he need to invest initially?

  19. Compound Interest EXAMPLE 6:Sarah is starting a small business. She applies for a $10 000 loan, which she plans to repay in 5 years. The amount Sarah will owe when the loan is due is $13439.16. What rate of interest, compounded semi-annually, is Sarah being charged?

  20. Compound Interest – Thinking? EXAMPLE 7: a) Nupurwants to invest $5000 for 6 years. The Bank of Hubba Bubba is offering 4 accounts. Which account should she invest in? Justify your choice. • 6% per annum • simple interest 2) 6% per annum compounded annually 3) 6% per annum compounded semi-annually 4) 6% per annum compounded monthly b) How long will it take for Nupur’sinvestment to double in value if she chose the account you found in part (a)?

  21. HomeFUN!!!  • Functions 11 Textbook!! • Pages 433 – 435 • # 1, 2, 5, 6, 9, 10, 11, 14

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