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Understanding Annuities: Definitions, Formulas, and Examples

Learn the basics of annuities, including simple and ordinary types, with practical examples for calculating future values and interest earned over fixed periods. Explore payment intervals, compound interest, and more!

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Understanding Annuities: Definitions, Formulas, and Examples

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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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