Albert Einstein's Rule of 72
You are planning to invest your money in some XYZ scheme, that provides an interest rate of r% compounded annually. How to calculate the number of years that it will take for your investment to double your value?
You are planning for retirement. You want to know at the end of say n years, what is the value of your total investments?
The question looks simple, use the Compund Interest Formula
Assume The interest rate is 8%, for your investment to double its value, A = 2* P
i.e:
Take log.
Do you think this is easy to calculate manually? Do you want a way to calculate this with out using a calculator? Proceed furthur.
Albert Einstein has discovered a simple formula - E=mC^2? No! It is much simpler than this. It is famously known as the rule of 72.
The formula is simple,
The number of years taken to get double your investment, N = 72 / r, where r is the rate of interest.
That is if the rate of interest is 8%, then it takes 72/8 = 9 years for your investment to get doubled. This we verified just now. Let us check for the next,
If the rate of interest is 12%, then it takes 72/12 = 6 years for your investment to get doubled.
To verify that, A = P(1 + 12/100)^6 = P*(1.12)^6 = P*1.97. That is at the end of 6 years, you have around 1.97 times the initial investment, that is approximately double your investments.
[I am choosing 12% because, US stock markets have returned historically at this rate in long term. Indian markets have returned above 15% in the past 20years. But with some mix of both stocks and debt funds, you can expect easily around 12%. Use this number for your financial calculations ]
Simple, right? Einstein Rocks!
One more way to use this formula. You are planning to invest for long term with an eye on your retirement. You want to know how much your money would have become when you retire. Do this way.
If your investment is able to return at 12% p.a, then it doubles every 6 years. It means in 30years, it would have double 5 times. It means your investment is mulitiplied by 2, five times.
that is you will have 2^5 = 32 times your current value.
1-->2-->4-->8-->16-->32
0 6 12 18 24 30
If your investment will be able to grow 15%p.a, simple mental calculations will do. 72/15 ~ 5 years. So in the same 30 years, your investment will become 2^(30/5) = 2^6 = 64 times.
Using the text book formula for compound interest and a calculator, your total amount comes as 66 times your initial investment, which is very close to our 30 second mental work!
Act smart. When some one speaks about financial planning or tax planning during your tea-break, the discussion will divert towards interest rates and actual returns, use this rule of 72 to surprise your friends with your amazingly spead calculations ;-)
You are planning for retirement. You want to know at the end of say n years, what is the value of your total investments?
The question looks simple, use the Compund Interest Formula
A = P*(1+r/100)^nLet us find the results in the text book way.
Assume The interest rate is 8%, for your investment to double its value, A = 2* P
i.e:
2*P = P*(1+r/100)^nHow to proceed furthur? 'n' is in exponent position...
2 = (1 + 8/100)^n
2 = 1.08^n
Take log.
log 2 = n log 1.08That is it will take 9 years for your investment to double if the interest rate is 8%.
n = (log 2)/log(1.08)
n = 0.3010/0.0334 = 9.011
n = 9 years approximately.
Do you think this is easy to calculate manually? Do you want a way to calculate this with out using a calculator? Proceed furthur.
Albert Einstein has discovered a simple formula - E=mC^2? No! It is much simpler than this. It is famously known as the rule of 72.
The formula is simple,
The number of years taken to get double your investment, N = 72 / r, where r is the rate of interest.
That is if the rate of interest is 8%, then it takes 72/8 = 9 years for your investment to get doubled. This we verified just now. Let us check for the next,
If the rate of interest is 12%, then it takes 72/12 = 6 years for your investment to get doubled.
To verify that, A = P(1 + 12/100)^6 = P*(1.12)^6 = P*1.97. That is at the end of 6 years, you have around 1.97 times the initial investment, that is approximately double your investments.
[I am choosing 12% because, US stock markets have returned historically at this rate in long term. Indian markets have returned above 15% in the past 20years. But with some mix of both stocks and debt funds, you can expect easily around 12%. Use this number for your financial calculations ]
Simple, right? Einstein Rocks!
One more way to use this formula. You are planning to invest for long term with an eye on your retirement. You want to know how much your money would have become when you retire. Do this way.
If your investment is able to return at 12% p.a, then it doubles every 6 years. It means in 30years, it would have double 5 times. It means your investment is mulitiplied by 2, five times.
that is you will have 2^5 = 32 times your current value.
1-->2-->4-->8-->16-->32
0 6 12 18 24 30
If your investment will be able to grow 15%p.a, simple mental calculations will do. 72/15 ~ 5 years. So in the same 30 years, your investment will become 2^(30/5) = 2^6 = 64 times.
Using the text book formula for compound interest and a calculator, your total amount comes as 66 times your initial investment, which is very close to our 30 second mental work!
Act smart. When some one speaks about financial planning or tax planning during your tea-break, the discussion will divert towards interest rates and actual returns, use this rule of 72 to surprise your friends with your amazingly spead calculations ;-)
posted by Jayaprabhakar | 11:16 AM
2 Comments:
u hav bcome a core finance guy..
keep it up
Oops..Probably the first person I will contact once I get my salary would be U..
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