# Math Help - Present Values

1. ## Present Values

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

2. Originally Posted by mukrosa
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 $i_{annual effective} = 0.08$

Define $i_{monthly effective} = 1.08^{1/12}-1$

Define $v = v_{monthly} = \frac{1}{1+i_{monthly effective}}$

The first payment is one year away from the valuation date.

$100(v^{12} + v^{13} + ... + v^{47})$

3. ## Not Sure

The payments were being made daily so mayb we ought to use[iΛ(364)][/]wat do u tnk?

To see where you're at, can you answer this:
what is the present value of a series of 12 monthly payments,
starting in 1 month from now, at 12% annual compounded monthly?

5. Often a monthly approximation is sufficient for payments made on the same day of each month.

Please be clear about the use fo the word "effective". Make sure you mean it.

6. the monthly effective rate=0.11386 then i assume value of payments is 1 [(1-vΛn)/i=(1-(1/1.11386)Λ12)/0.11386=6.37469][/MATH

7. Originally Posted by mukrosa
the monthly effective rate=0.11386 then i assume value of payments is 1 [(1-vΛn)/i=(1-(1/1.11386)Λ12)/0.11386=6.37469][/MATH
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%)