Time Value of Money Question

M

monroeins

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Jan 15, 2011
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Hello,
I am trying to calculate what the present value of a stream of money that reduces by 10% annually. For example today I get $100, one year later $90, the following year $81....

I looked up the Time Value equations on wikipedia but can't quite figure it out because the payment period is infinite. 5% interest rate is fine.

Any help would be greatly appreciated.

Thanks!

-Drew
 
Many, many such problems can be solve by "Basic Principles".

Define Everthing.

Starting Payment = P = $100
Payment Decrease = r = 0.90
Interest Discount @ 5% = v = 1/(1.05)

Now, just build all the payments:

\(\displaystyle P + Prv + Pr^{2}v^{2} + Pr^{3}v^{3} + Pr^{4}v^{4} + Pr^{5}v^{\5} + Pr^{6}v^{6} + Pr^{7}v^{7} + etc\)

The task is to add them all up.

\(\displaystyle P(1 + rv + r^{2}v^{2} + r^{3}v^{3} + r^{4}v^{4} + r^{5}v^{\5} + r^{6}v^{6} + r^{7}v^{7} + etc)\)

\(\displaystyle P(1 + rv + (rv)^{2} + (rv)^{3} + (rv)^{4} + (rv)^{\5} + (rv)^{6} + (rv)^{7} + etc)\)

You should recognize the standard Infinite Geometric Series

\(\displaystyle P\cdot\frac{1}{1-rv}\)

The important part was in the initial definitions.
 
in 93 years: .0055533... ; a penny when rounded
in 94 years: .0049979... ; hmmm :roll:
 
Denis said:
in 93 years: .0055533... ; a penny when rounded
in 94 years: .0049979... ; hmmm :roll:
Click to expand...

Start paying in rupees, pesos or liras.....
 
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