How do we calculate CAGR of many years but at today’s money value?

[medengconfused]

Rs. 1,00,000 invested at 12% CAGR for 15 years is going to become around Rs. 5,50,000.

But how to calculate such that we can see the final amount in today’s value by omitting inflation?

If inflation is 7% pa, do we then say it’s growing at a CAGR of 5% from a pure profit point of view (ignoring taxes)?

So then can we say that in 15 years, from the purchasing power standpoint of today, this 1,00,000 becomes 2,10,000 at 5% cagr? Is this a flawed calculation?

Disclaimer: Clearly, I’m horrible at maths. So be nice.

Edit: turns out, I’m not that horrible at maths

 

[monte]

@medengconfused You are not completely wrong with the calculation but slightly off base with regards to how you got the answer.

The part that you got right ,was subtracting inflation from the CAGR, but that's a calculation approximation in reality what you need to do is adjust the present value.

If you start with 1 rupee today and have a 12% CAGR then after 15. Years your value, as you rightly calculated is , 1* (1+0.12)[sup]15[/sup] which is approximately 5.5 rupees

To calculate the effect of inflation, which is also compunding by the way, you have to adjust your clauclation like this

(1* (1+0.12)[sup]15[/sup] ) / (1+0.07)[sup]15[/sup]

That's how you account for inflation. Now as it turns out

1.12/1.07 is very close to 1+( .12-.07) mathematically (1.046 to be precise)

That's just a consequence of binomial expansions etc and hence easy to use.

But if your time periods are longer like in your case, the error in approximation also compunds and when dealing with large number it can cause errors in the order of lacks.

So yea,your intuition was correct, your inference is correct as well just that the intuition led you to the approximatiom of the math rather than the actual one

 

[linlin]

@monte Samajh Nahin Aaya per sunkar Achcha Laga

 

[oxtailsoup]

@monte Where's that award when we need it..

None the less

 

[aellagirl]

@monte Pls remove stray bracket to avoid confusion

 

[monte]

@aellagirl Sorry, the reddit formatting is wonky ..fixed one

 

[tomwedding]

@medengconfused That is not how compounding works.

1. You calculate the value of 1 Rs. growing at 12% per annum in 15 years, ie: Rs. 5.4736

1. You calculate the value of 1 Rs. growing at 7% per annum in 15 years, ie: Rs. 2.759
2. Now you divide 1 with 2 ie you get a ratio of 1.9839.

This means your real money has almost doubled in 15 years. Think of interest rates as accelaration. A car accelerating at 7% per annum will be left further and further behind by a car accelerating at 12% per annum.

Edit: Wrote 15% by mistake. It’s 12%. At 15% cagr, the money triples in 15 years

 

[valarie51899]

@tomwedding This is correct but my disappointment is immeasurable and my day is ruined.jpg
12% cagr and still taking 15years to actually double the value is so painful to realize.

 

[tomwedding]

@valarie51899 It is 12%. At 15%, the money triples. Sorry for the mistake

 

[godisiam]

@medengconfused If you say it’s growing at a CAGR of 5% (12% - 7%), you’d get a crude approximation. If you want a precise value, you should say it’s growing at 4.67% ((1 + 12%)/(1 + 7%) - 1).

In general, the formula is [ (1 + growth rate)/(1 + inflation rate) - 1 ]

 

[leaniemeanie]

@godisiam Yeah as a thumb rule for inflation calculations in investments it is factor* factor or factor/factor.

 

[deepabently]

@medengconfused I think what you are looking for is "Real Returns". At 7% inflation, 1,00,000 15 years ago is equal to 2,70,000 today. You have to calculate at what CAGR 2,70,000 becomes 5,50,500 in 15 years.

So solve for r in the below equation:

5,50,000 = 2,70,000 (1 + r/100)[sup]15[/sup]

The answer should be pretty close to 5%

 

[paints]

@medengconfused It looks like you thoroughly understand how inflation can sneakily alter the game. Okay, so picture this- you throw Rs. 1,00,000 into the investment pool at a cool 12% CAGR for 15 years, and voila, you see a nominal value of Rs. 5,50,000.

Not bad, right? But hold up!

This amount is playing hard to get because it's not adjusted for inflation. So, let's spice things up. We'll sprinkle in a 7% annual inflation rate to really see what's going on. Cue the adjusted future value calculation magic: Adjusted Future Value = Future Value / (1 + Inflation Rate)^(Number of Years). Crunching the numbers, the adjusted future value, with a 7% annual inflation twist, lands us at a cool Rs. 2,10,000.

Now, here's the real talk – if you dropped Rs. 1,00,000 into this investment adventure today, considering the inflation factor, it would be flexing a purchasing power of Rs. 2,10,000 in 15 years. Remember, it's not just about the flashy Rs. 5,50,000; the real champ, adjusted for inflation, is Rs. 2,10,000.

That's the game-changing insight to truly understand the impact of your investment in the wild world of inflation!

 

[snowgi7574]

@medengconfused If both appreciation (15%) and depreciation due to inflation (7%) is realized after a period of 1 year, then your effective return is (1+0.15)*(1-0.07)=1.0695, which means there is an effective growth of 6.95% every year. Thus, in a span of 15 years, you would have Rs.2,73,976/- in today’s value.