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Unformatted text preview: MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Name: Two points . Professor : Stephen Suen Section: Peer Leaders : Hana Aboul-Hosn, Toni Jung, Renan Mendonca 10. Compound interest: savings, annuities, and debts . Compound interest is a friend for savings, but it becomes a great burden for debts. We shall study its effects on credit card debts. Most banks compound interests daily. Since compounding daily has nearly the same effect as compounding continuously, we shall simply assume that interest is compounded continuously. We verify this with the following example. Example . (Compound interest.) Compute the future values of a $1000 investment after t = 20 years, with annual interest rate r = 0 . 08, when (a) interest is compounded daily (assuming 365 days in a year), and (b) interest is compounded continuously. Solution. (a) For interest compounded daily, we use the formula A = P parenleftBig 1 + r n parenrightBig nt = 1000 parenleftbigg 1 + . 08 365 parenrightbigg (365)(20) = $4952 . 16 . (b) For interest compounded continuously, we have A = P e rt = 1000 · e (0 . 08)(20) = $4953 . 03 . We remark that the two future values are very similar. An (ordinary) annuity is a stream of payments at regular intervals over a specific amount of time. The next example guides us to obtain a formula for the future value A of an annuity (when interest is compounded continuously)....
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.
- Fall '08