Find present value as at january 2009 of a series of payments of 100 payable on first day of each month during years 2010,2011,2012. Assume effective rate of interestof 8% p.a
Why is that funny? Would it be less or more funny if it were 7%?
You MUST learn "Basic Principles".
Define $\displaystyle i_{annual effective} = 0.08$
Define $\displaystyle i_{monthly effective} = 1.08^{1/12}-1$
Define $\displaystyle v = v_{monthly} = \frac{1}{1+i_{monthly effective}}$
The first payment is one year away from the valuation date.
$\displaystyle 100(v^{12} + v^{13} + ... + v^{47})$
Can you add them up?
NO. "12% annual compounded monthly" means 1% per month, so 1.01^12 - 1 = .126825 (12.6825% effective).
You assumed "12% effective annual compounded monthly", or:
(1 + i)^12 = 1.12 ; i = .009488... ; i * 12 = .11386...
Even at that, you need to use .009488 in your calculation, not .11386:
[1 - (1 / 1.009488)^12] / .009488 = 11.2915...
So, using $100 per month, present value is $1129.15
Your original problem states: "Assume effective rate of interestof 8% p.a".
The word "effective" means (1 + i)^12 = 1.08.
If instead it was: "Assume rate of interestof 8% p.a compounded monthly", then:
effective annual rate = (1 + .08/12)^12 - 1 = .0829995... (~8.3%)