# Re: Annuity

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Posted by Denis Borris on September 27, 2002 at 03:09:07:

In Reply to: Annuity posted by Orio's on September 26, 2002 at 23:57:18:

: Here is a little question here i need advice on to see if i'm correct:
: Each tuesday from tuesday 11 May 1999 until tuesday 16 November 1999 inclusive, Mr Hancox deposited \$70 in a Xmas savings account. The interest rate was 8% per annum, compounding daily. What should have been the balance of the account on Tuesday 7 Dec 1999, i.e. 3 weeks after the last payment? (there were 28 deposits altogether).
: here is what I did, but I don't know if I'm correct or not.
: 1) 0.08/365=0.0002191780822
: 2) 70*((1+0.0002191780822)^28-1)/0.0002191780822
: =1965.810462
: 3) FV=1965.810462*1.0002191780822^3
: =1967.103333

70*(1+0.0002191780822)^28 is definitely incorrect: that's paying the poor guy
the daily rate every 7 days!
8% annual cpd daily means a "true effective" rate of 8.327757....%;
divide that by 52, to match the weekly deposits; this will result in a balance
of 2.002.97 AT THE DATE OF 28th deposit; then do the add'l days.

Your teacher may not quite agree with that....BUT turn him over to me!
The problem as it is worded is not really complete (not in Canada anyway!);
like, is whatever interest "has compounded daily" for a week deposited along with
the 70 bucks?
This would mean that: nominal interest of 8% annually is compounded daily
and credited weekly.

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