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PERSONAL FINANCE

PERSONAL FINANCE. MBF3C Lesson #3: Compound Interest. Some notes about simple vs. compound Interest. Simple interest is a linear relation. Interest is only earned on the original principle.

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PERSONAL FINANCE

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  1. PERSONAL FINANCE MBF3C Lesson #3: Compound Interest

  2. Some notes aboutsimplevs. compound Interest • Simple interest is a linear relation. Interest is only earned on the original principle. • Compound interest is exponential. Interest is earned not only on the original principle but also on the interest which has been earned so far. • The difference between simple and compound interest is very small over a short period of time. However, unlike simple interest, if you earn compound interest, the amount of interest continues to increase over time. Over a long period of time, the interest earned in compound interest is much larger than the interest earned with simple interest.

  3. The time interval between the occasions at which interest is added to the account is called the compounding period . The chart below describes some of the common compounding periods:

  4. Rather than using a table or a graph to see how the value of an investment grows, you can use a formula.

  5. P is the principal, or initial value. • A is the accumulated amount or future value. • iis the interest rate per compounding period. • n is the number of compounding periods.

  6. The table shows how to convert the yearly interest rate and term for various compounding periods. *continued on next slide

  7. WHAT EXACTLY DOES THE “i” MEAN? Interest rate as a decimal number of times per year that interest in compounded

  8. WHAT EXACTLY DOES THE “n” MEAN? Number of times per year that interest is compounded per year x Number of Years

  9. Example:Interest Compounded Semi-Annually • Determine how much money you will have if $500 is invested for six years, at 4% per year, compounded semi-annually. Solution • Interest is compounded semi-annually, meaning twice a year, for six years. There are 2 × 6, or 12, compounding periods. This can be illustrated on a timeline.

  10. Determine how much money you will have if $500 is invested for six years, at 4% per year, compounded semi-annually. i= 0.04 ÷ 2 = 0.02 n = 6 × 2 = 12 P = 500 A= 500(1+0.02)12 = 634.12 After six years, you will have $634.12.

  11. Example:Interest Compounded Monthly • Alice borrowed $5000 to start a small business. The interest rate on the loan was 9% per year, compounded monthly. She is expected to repay the loan in full after four years. a) How much must Alice repay? b) How much of the amount Alice repays will be interest?

  12. A) How much must Alice repay? Alice borrowed $5000 to start a small business. The interest rate on the loan was 9% per year, compounded monthly. She is expected to repay the loan in full after four years. • Interest is compounded monthly, meaning 12 times a year, for four years. There are 12 × 4, or 48, compounding periods.

  13. Alice borrowed $5000 to start a small business. The interest rate on the loan was 9% per year, compounded monthly. She is expected to repay the loan in full after four years. i= 0.09 ÷ 12 = 0.0075 n = 4 × 12 = 48 P = 5000 A= 5000(1+0.0075)48 = 7157.03Alice must repay $7157.03 after four years

  14. B) How much of the amount Alice repays will be interest? • Calculate the total interest by subtracting the principal from the amount. 7157.03 - 5000 = 2157.03 Therefore, Alice will pay $2157.03 in interest.

  15. Key Concepts (p. 432) • Compound interest can be accumulated at various intervals, such as annually, semi-annually, quarterly, and monthly. • The compound interest formula A = P(1 + i)n can be used to calculate the future value, or amount – A is the future value or accumulated amount of an investment or loan. – P is the principal. – iis the interest rate, in decimal form, per interest period. – n is the number of compounding periods.

  16. IN-CLASS & HOMEWORK Page 432, # 1ace, 2bc, 3bd, 4, 5, 7, 8abcd

  17. SUCCESS CRITERIA FOR THIS LESSON: I can • ____ Calculate the number of compound periods (n) and periodic interest rate (i) • ____ Calculate the future amount or value of an investment using compound interest compounded over different periods • ____ Calculate the interest earned on an investment

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