Actuarial Outpost Nov 2000 #9
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#1
05-09-2004, 01:15 PM
 FrankieY18 Member Join Date: Sep 2003 Posts: 458
Nov 2000 #9

Victor invests 300 into a bank account at the beginning of each year for 20 years. The account pays out interest at the end of every year at an annual effective interest rate of i%. The interest is reinvested at an annual effective rate of (i/2)%.

The yield rate on the entire investment over the 20 year period is 8% annual effective. Determine i.

The solution says:
300 s (double dot) 20 | 8% = 20 (300) + 300i (Is) 20 | i/2%
14826.88 = 6000 + 300i (s 21 | i/2% - 21) / (i/2)

why did they change (Is) 20 to 21????
#2
05-09-2004, 01:26 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,452

Did they change (Is)20 to (Is)21?

Or did they use a formula for (Is)20 in terms of s_immediate rather than s_due?
#3
05-09-2004, 01:43 PM
 FrankieY18 Member Join Date: Sep 2003 Posts: 458

they didn't say anything...
that's exactly what the solution says and then that's how they solve it from there
#4
05-09-2004, 02:02 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,452

That was my point: You seem to think they changed (Is)20 to (Is)21. Why?

Aren't both of these formulas valid:
(Is)_immediate_20 = (s_due_20 - 20)/i
and
(Is)_immediate_20 = (s_immediate_21 - 21)/i?

If both formulas are valid ways to evaluate (Is)_immediate_20, I don't see how we can probe into their minds to decide why they chose the version they did. They needed to evaluate (Is). They evaluated it.
#5
05-09-2004, 05:26 PM
 FrankieY18 Member Join Date: Sep 2003 Posts: 458

gotcha...

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