My Math Forum Annuity Problem

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 September 15th, 2009, 12:00 PM #1 Newbie   Joined: Sep 2009 Posts: 4 Thanks: 0 Annuity Problem a) Julie deposits $12 into an account at the end of each day in 1989 and 1990 and$15 at the end of each day in 1991. The account earns an annual effective interest rate of 9% in 1989 and 1990 and an annual effective interest rate of 12% in 1991. Find the amount in Julie’s account on December 31, 1991. (Answer: $16,502.5 b) Rework part (a) using the approximation that the deposits are made continuously. (Answer:$16,504.75) For part a), my initial reaction was that it would be something like 12[(1.09)^730 - 1 / .09] + 15[(1.12)^365 - 1 / .12] ...but this obviously gives ridiculous numbers so I'm not sure how else to go about it. Thanks for any help!
 September 15th, 2009, 01:42 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Annuity Problem You assumed 9% daily interest; it should be yearly. I would assume (but check this!) that the problem means that the account earns interest daily at a rate that makes (1 + r/365)^365 = 1.09.
 September 15th, 2009, 03:03 PM #3 Newbie   Joined: Sep 2009 Posts: 4 Thanks: 0 Re: Annuity Problem Ok so part (a) = (1.12)(12)[(1.000236)^730 - 1 / .000236] + 15[(1.000311)^365 - 1 / .000311] = 16502.58 which gives me the right answer but I don't understand how part (b) is set up differently?
 September 16th, 2009, 07:10 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Annuity Problem You know continuous interest, right? P * exp(r * t). A day's continuous interest at yearly rate r multiplies the principal by exp(r / 365).

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