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Compound Interest

Compound Interest. Compound Interest. OR. The interest is added to the principal and that amount becomes the principal for the next calculation of interest.

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Compound Interest

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  1. Compound Interest

  2. Compound Interest OR The interest is added to the principal and that amount becomes the principal for the next calculation of interest.

  3. Interest Period (compounding Period): The amount of time which interest is calculated and added to the principal. It could be a year, a month, a week and so on.

  4. Find the period interest rate for: • A 12% annual interest rate with 4 interest periods per year. • 3% • An 18% annual rate with 12 interest periods per year. • 1 ½ % • An 8% annual rate with 4 interest periods per year. • 2%

  5. Find the Future Value Using the simple interest formula method: • Find the end of period principal: multiply the original principal by the sum of 1 and the period interest rate. • For each remaining period in turn, find the next end of period principal: multiply by the previous end of period principal by the sum of 1 and the period interest rate. • Identify the last end-of-period principal as the future value.

  6. Look at this example Find the future value of a loan of $800 at 13% for three years. • The period interest rate is 13% since it is calculated annually. • First end-of-year = $800 x 1.13 = $904 • Second end-of-year =$904 x 1.13 = $1021.52 • Third end-of-year = $1021.52 x 1.13 = $1,154.32 • The FV of this loan is $1,154.32

  7. Find the compound interest • Compound interest = future value – original principal. • In the previous example, the compound interest is equal to the future value – original principal. • CI = $1,154.32 - $800 = $354.32 • The compound interest = $354.32

  8. Derivation of the Formula

  9. Examples • If 500$ were deposited in a bank savings account, how much would be in the account three years hence if the bank paid 6% interest compounded annually?

  10. Examples • If you wished to have 800$in a savings account at the end of four years, and 5% interest was paid annually, how much should you put into the savings account now?

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