# Capital Gains Backwards

#### rayss

From: Ray Summerton

Investors talk about long term capital gains being say 10% a year over 7years, doubling the value of a property. Can you mathematicians out there tell me how you work capital gains backwards? I.E. Suppose I bought a house for \$50k back in 1978 and it is now valued at 200k. What is the CG achieved taking into account compounding interest? Or is this only for top notch accountants, or do you just divide the gain by the number of years and get an average?
Regards Ray

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##### Guest
From: Sergey Golovin

Ray,
Number of years by number of dollars

200K-50K=150K
2001-1978=23 years
150/23=6.5K per year

and in percentage terms (deepens on you calculator - punch in "200" then "-" then "6" then "%" look at the answer and then "-" "6" "%" look at the answer and "-" "6" "%" .....22 times later you will get to the original purchase prise)

1.200K-6%=188K
2.188K-6%=176K...
22 years back
22.54K-6%=51K

Would be about 6%? I hope it is right?

Serge.

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##### Guest
From: Donna Larcos

Or you can buy a BA-35 solar calculator
from Texas Instruments which does this
for you in about 10 seconds.

(I knew there was a reason I gave up
Maths in year 10)

Donna

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##### Guest
From: James Johnson

I'm not sure if I'm repeating what Sergey just said, but there is a formula for it which means less calculator time.

A = A(0) * [1 + R/100]PWR (n)

Or R =[[A/A(0)]PWR (1/n)]-1

where R= compound capital gain rate,
A= Property price now (200k)
A(0)= Property price back then (50k)
n= number of elapsing time intervals (ie 23 yrs)
(and PWR=power).

Looks a lot more complicated than it was meant to- computers have that effect

It comes out to about 6.2%

Jimmy

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##### Guest
From: Scott Elsom

Looks like Donna has read Buffetology!

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#### rayss

From: Ray Summerton

Thanks Guys and Gals, and especially Chris for the spreadsheet. What a big help it is to know there are others out there who are prepared to help newbies to get a handle on a better and less taxed "superannuation" system. Although the sales tax on each purchase is a big downer in S.A. and the extra costs added to the purchase price reduces the capital gains percentage in the long run.
Regards Ray

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##### Guest
From: Simon B

Hi,

This formula works a treat on Excel -

EXP(LN(200 000/50 000)/23) - 1

Then convert the cell to %

The EXP and LN are maths functions that Excel uses happily.

Have a good one,

Simon B

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