Present Values

mukrosa · #1 $Old$ November 4th, 2009, 01:19 PM

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

TKHunny · #2 $Old$ November 4th, 2009, 05:28 PM

Quote:

Originally Posted by mukrosa $View Post$

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.

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

Can you add them up?

mukrosa · #3 $Old$ November 4th, 2009, 08:31 PM

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

Wilmer · #4 $Old$ November 4th, 2009, 09:15 PM

Please get your problem CLEAR, then post it again

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?

TKHunny · #5 $Old$ November 4th, 2009, 11:07 PM

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.

mukrosa · #6 $Old$ November 4th, 2009, 11:41 PM

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

Wilmer · #7 $Old$ November 5th, 2009, 07:31 AM

Quote:

Originally Posted by mukrosa $View Post$

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%)