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Compound Interest

Compound Interest. Making or Spending Money. Simple Interest Formula. If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r , expressed as a decimal, then interest I charged is

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Compound Interest

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  1. Compound Interest Making or Spending Money

  2. Simple Interest Formula • If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed as a decimal, then interest I charged is • This interest is not used very often. Interest is usually compounded which means interest is charged or given on the interest and the principal. • Simple Interest Example

  3. Compound Interest • Payment Periods: • Annually Once per year • Semiannually Twice per year • Quarterly Four times per year • Monthly Twelve times per year • Weekly Fifty two times per year • Daily 365 (360 by banks) per year

  4. Compound Interest Formula • The amount A after t years due to a principal P invested at an annual interest rate r compounded n times per year is • A is commonly referred to as the accumulated value or future value of the account. P is called the present value.

  5. Compound Interest • Example: • Investing $1000 at an annual rate of 8% compounded annually, quarterly, monthly, and daily will yield the following amounts after 1 year: • Annually • Quarterly • Monthly • Daily

  6. Compound Interest • On-line example • More on-line examples

  7. Compound Interest • Tutorial

  8. Continuous Compounding The amount A after t years due to a principal P invested at an annual interest rate r compounded continuously is

  9. Finding Effective Rate of Interest • Definition • Steps for Finding ERI: (If a P is not given, use $100) • Find the value of the interest compounded annually for one year • Find the value of the interest compounded for the given amount of times annually • Find the interest by subtracting (Step 2 – original principal) • Divide the answer by the original principal (if using 100 don’t have to because it’s already written as a percent).

  10. Effective Rate of Interest • Finding Interest Video • What is the Effective Rate of Interest for 5.25% compounded quarterly? • Step 1: 100(1 + .0525)(1) = A • A = 105.25 • Step 2: • Step 3: 105.35 – 100 = 5.35 • Step 4: 5.35%

  11. Present Value Formulas • The present value P of A dollars to be received after t years, assuming a per annum interest rate r compounded n times per year, is

  12. Examples • Sears charges 1.25% per month on the unpaid balance for customers with charge accounts (interest is compounded monthly). A customer charges $200 and does not pay her bill for 6 months. What is the bill at that time?

  13. Examples • Tracy is contemplating the purchase of 100 shares of stock selling for $15 per share. The stock pays no dividends. Her broker says that the stock will be worth $20 per share in 2 years. What is the annual rate of return on this investment?

  14. Examples • Will invests $2000 in a bond trust that pays 9% interest compounded semiannually. His friend Henry invests $2000 in a certificate of deposit (CD) that pays 8.5% compounded continuously. Who has more money after 20 years, Will or Henry?

  15. Examples • How long will it take for an investment to double in value if it earns 5% compounded continuously?

  16. Examples • What annual rate of interest compounded annually should you seek if you want to double your investment in 5 years?

  17. Examples • On-line problems • More on-line examples

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