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September 15th, 2009, 12:00 PM   #1
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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!
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September 15th, 2009, 01:42 PM   #2
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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.
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September 15th, 2009, 03:03 PM   #3
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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?
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September 16th, 2009, 07:10 AM   #4
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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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