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Understanding Annuities: Future Value of Periodic Deposits in Mathematics - Mat 112

Learn how to calculate the future value of periodic deposits known as annuities using geometric sum formula. Discover the interest earned, future value formula, and examples for practical application in Mat 112. Explore solving for PMT and determining the total amount with step-by-step guidance.

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Understanding Annuities: Future Value of Periodic Deposits in Mathematics - Mat 112

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  1. Annuities – the “Future Value”of periodic deposits Mat 112

  2. First, a note To compute a particular type of sum (a “geometric sum”), where the terms are powers of some number, such as: The total is simply given by

  3. Annuities

  4. Forming a “future value”

  5. Making Deposits

  6. First Deposit

  7. Second Deposit

  8. And so on…

  9. …for a total of ?

  10. Interest Earned?

  11. Future Value formula Why? Results from determining the geometric sum.

  12. Given FV, find PMT

  13. FV formula

  14. Examples for Future Value Mat 112

  15. FV Example

  16. How much interest?

  17. PMT Example

  18. Calculate carefully! PMT = $104.31 (or round up to $104.32 to be safe)

  19. Example: “quarterly deposits”

  20. Example: “IRA”

  21. Solving for n? Mat 112

  22. A Bigger Challenge?

  23. Or simply, Using the Log…

  24. Bring down the exponent

  25. Not Another Formula? Although the text offers this result as a new formula and we could memorize It seems more reasonable to just solve this exponential equation in the usual way.

  26. Does it Check?

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