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The Amount of an Annuity

The Amount of an Annuity. Definitions. An annuity is a series of equal payments or deposits earning compound interest and made at regular intervals over a fixed period of time A simple annuity is one for which the compounding period is equal to the payment period

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The Amount of an Annuity

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  1. The Amount of an Annuity

  2. Definitions • An annuity is a series of equal payments or deposits earning compound interest and made at regular intervals over a fixed period of time • A simple annuity is one for which the compounding period is equal to the payment period • An ordinary annuity is one for which the payments are made at the end of each payment period

  3. Example: • Kramer is saving for the down payment on a new house. He plans to deposit $5000 at the end of each year for 4 years. If interest is 6% per year compounded annually, determine the amount that will be in his bank account after 4 years.

  4. TIMELINE • 0 1 2 3 4

  5. FORUMLA: • FV = Future Value • PMT = annuity payment made every period • i = interest payment per period • n = # of payments(# of compounding periods)

  6. Example Calculation • i = 0.06 • n = 4

  7. Example 2: • Lucy makes regular payments of $100 at the end of each month for 30 years. If interest is 2.5% per year compounded monthly, how much money does Lucy have at the end of this time? How much interest does she earn?

  8. Example Calculation • i = 0.025/12 = .002083333 • n = 30 x 12 = 360

  9. Interest Earned: • = FUTURE VALUE – AMOUNT PAID • = 53 536.75 – 360 X 100 • = 53 536.75 – 36 000 • = $17 536.75

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