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#1
04-26-2012, 08:05 PM
 azul673 SOA Join Date: Mar 2012 Posts: 2
Question about Problem in Finan FM book

I'm having a hard time coming up with the answer given for this problem. It's 6.6 in Finan.

An amount of money is invested for one year at a rate of interest of 3% per
quarter. Let D(k) be the diﬀerence between the amount of interest earned
on a compound interest basis, and on a simple interest basis for quarter k,
where k = 1, 2, 3, 4. Find the ratio of D(4) to D(3).

Here's what I'm getting:
Set A(0) = 100
i(1) compound = 3
i(2) compound = 106.09 - 103 = 3.09
i(3) compound = 109.2727 - 106.09 = 3.1827
i(4) compound = 112.55 - 109.2727 = 3.2773

i simple = 3 for all periods

so D(4) = .2773
D(3) = .1827

D(4)/D(3) = 1.5178

#2
04-26-2012, 08:15 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 30,796

Easy: carry i(4) compound to 2 more digits, to same accuracy as i(3) compound
#3
04-26-2012, 08:54 PM
 azul673 SOA Join Date: Mar 2012 Posts: 2

Yes, got it! Thank you!