## 3 most Important formula’s you should know – Compound interest, CAGR and Annuity calculator with example

**1. Compound Interest**

This formula is often used to calculate the returns some investment has given. The main concept in compound interest is that interest gets accumulated with the total principal amount and that interest again earns interest over the years. Which makes it very powerful.

**Formula : A = P * (1+r/t)^(nt)**

Where,

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

A = amount after time t

**Example 1 :**

Investment = Rs.10,000

return = 9%

investment period = 8 years

Total amount = 10000(1+.09)^8 = 19925.63

**Example 2 :**

Sensex returned 17.3% return over 29 years since its inception in 1979. What would be worth of Rs 10,000 invested that time.

A = 10,000 * (1+.173)^29 = 1022450.64 (10 lacs)

You can see that a small amount has actually grown to 100 times.

**Compound interest Calculator : **

https://math.about.com/library/blcompoundinterest.htm

## 2. CAGR

This tool is very important because it helps in comparing two differnt returns from two investments, you can calculate how much an investment has returned per year on compounded basis, Its just the opposite of Compound interest

**Formula : CAGR = (A/P)**^{1/n} – 1

^{1/n}– 1

where:

A = Final amount

P = amount invested

n = Number of years

CAGR can be a great tool to compare two different investments and there returns.

**Example :**

A. 10,000 invested in a XYZ mutual fund for 2 yrs became 20,000

B. 50,000 invested in GOLD for 7 years became 4,00,000

### Which investment has given more returns?

Here the main doubt is that how to calculate which one is better .. the amount, tenure is different. So in this case we calculate and see CAGR, one with more CAGR will be good.

A) CAGR = 41.42 %

B) CAGR = 34.59 %

So, investment in A is better than B. Which is –

**CAGR calculator : **

https://www.moneychimp.com/calculator/discount_rate_calculator.htm

## 3. Annuity

This formula is very very important one, in our daily life we come across many situation where we do a fixed payment at the fixed interval, and we want to calculate the returns, but we don’t know how to do it .. Example can be

- Monthly payments in Mutual funds through SIP
- Yearly payment in a PPF.

Or any investment at a fixed inteval over some years. In that case we calculate the Final value using formula called Annuity.

**Formula : A = P * [{(1+i)^n – 1 }/i] * (1+i) (if payment are being made at the start)**

** (it will be P * [{(1+i)^n – 1 }/i] if payments are made at the end of the year)**

Where :

A = final amount

P = installment each time

n = total number of installments

i = interest rate for that tenure (example if yearly return is 24%, but payments are made monthly then i = 24/12 = 2%)

**Example 1 :**

Robert invests 10,000 each month in a mutual fund for 10 years and the annual return was 18%, what will be his final corpus?

Here as payments are monthly, total payment will be 10 * 12 = 120

so n = 120 and i = 1.5 % (18/12)

A = 10,000 * [{(1+ .015)^120 – 1}/.015 ] * (1+ .015) => 40,39.241 (40 lacs)

**Example 2 :**

Vikas is planning his retirement, and planning to invest 5,000 per month in a Mutual fund for 20 yrs where he expects a return of 15%, then take out all the amount after 20 yrs and then put it in a FD for 15 yrs which gives him 9.5% return.

Here, we there are two parts

A. He makes monthly payment for 20 yrs (here we have to apply annuity)

B. then he takes the money out after 20 yrs and then put it in FD for 15 yrs (as this is one time payment, here we will apply compound interest)

A ) n = 240 and i = 1.25% (as the payment are monthly)

His money after 20 years = [5,000 * (1 + .0125)^240 – 1) / .0125] * ( 1.0125) = 75,80,000 (75 lacs)

Now he invests this money into a FD for 15 yrs at 9.5%.

B) Final amount = 75,80,000 * (1.095)^15 = 2,95,00,000 (2.95 crores OR 29.5 millions)

So his final corpus will be 2.95 crores.

I need formula to calculate SIP approximate amount

Amount Per month * 12 * ((1.12)^number of years – 1)/.12

Dear Manish,

I am 39 years old engineering professional, looking into investment of tune 3000-4000/- per month in SIP for my future goals, please advise which SIPs is better performing etc.

With Regards,

Manish Goyal

There is always mutual funds who have already performed well, you can never guarantee future, but some good picks can be suggested to you at our Q&A forum – http://www.jagoinvestor.com/forum

Dear Manish Chauhan, Thanks for your informative article. The only request is that before posting an authentic article check twice or thrice. The reason is we are not expert in finacial matters. We simply follow the experts directives when we need a fiancial guidance. It should not happened in future that after reading your article waite for other experts commend. Wishing a successful carreer.

Not sure why you made that comment , Is any thing wrong in the article ? Please point it out to me !

I am not sure of your comment, which part you feel is unauthentic ?

Manish, I think he is referring to mistakes in the formula in the article. I still see you have not corrected it in the main article above. Request you to correct it so that nobody will pin point our dear Manish again 🙂

Will do 🙂

First of all, this is a very great article! thanks for writing!

While trying to find how much money a particular MF will make, I came across your article. I see websites like moneycontrol, valueresearchonline show CAGR of the MF for different years. I did some calculation and want to verify if they are correct….if not, then what is the correct way to work with them…

Say I invest 10,000 in an FD@ 8%/annum for 5 yrs and same 10,000 in a MF ( Birla Sunlife Frontline Eq) with the CAGR for 5 yrs @ 7.7% ( Source MoneyControl). So according to my calculation, the FD gives: 14,693 and the MF gives 14,490. Even if you deduct TDS from the FD, the overall returns are not that great!! Am I missing something here

The only thing is FD returns are guaranteed and predictable, while Mutual funds are not . You might have looked at the past 5 yrs return ,but thats not always the same .. if you have looked in 2008 , the past 5 yrs return would be close to 30% per annum 🙂 .

Thanks Manish for this fantastic article.

Are all formulas updated and can i use these formulas to calculate my investment plans?

Yes you can use these

Sir I follow you a lot you are my IDOL , ANGEL , ZODIAC SIGN , LUCKY PLANET MY MOON , SUN everything.

Thanks Manish

Excellent blog, Manish. Most topics are quite informative.

Looks like there is a minor error in the Compound Interest formula. Shouldn’t it be A = P * (1+r/n)^(nt)?

Yea thats correct . looks like I made a mistake .

Hi Manish,

Looks like the formulae is still the same. Can you please correct it… It should be r/n rather than r/t

Thanks

This is really helpful for a salary holder like me.

Sujith

Goodto know that !

Correction in SIP formula:

(10000*(((1+18%/12)^(10*12))-1))/(18%/12) = 3312881.91

(5000*(((1+15%/12)^(20*12))-1))/(15%/12) = 7486197.40

Anonymous

Thats correct. . but which one is wrong in the arrticle ? I have assumed the payments made in the start of the months and hence (1+r) is multiplied extra

Manish

Hi Manish,

Just wondering whether CAGR and ‘annualized return’ are same? Kindly confirm 🙂

CAGR is initial and final amount, and year difference between them. We find the compounded annual return using that initial amount which became the final amount over a period of time.

I have seen ‘annualized return’ term in Mutual fund performance report.

Thank you,

Balbir

Balbir

Yea they are same . CAGR is a fancy name to scare people 🙂

Manish

First things first, AMAZING blog. Kudos…came to know a lot about financial planning.

Also you acknowledged the typo in the compound interest formula but did edit your blog entry yet???

Rajesh

The formula is corrrect , I made a calculation mistake it seems last time 🙂

Manish

First let me appreciate your hard work . I am learning lot of thing through your blog which i should have learned very back 🙁

is there any formula where we can calculate rate of intrest for LIC policy?

For eg. Suppose i hav 2-3 lic policy and i want to calculate what rate of intrest i am getting after maturity of my policy?

Mahesh

thanks , For returns from LIC ,there is no special formula especially for LIC policies , but there is something called as IRR and XIRR , which is a general concept which you can use to calculate LIC policies returns , http://jagoinvestor.dev.diginnovators.site/2009/08/what-is-irr-and-xirr-and-how-to.html

Manish

[…] Sensex Return ChartSensex has returns close to 18% CAGR in the long term till date for One time investment and SIP investment […]

@Anonymous

Yup .. its a typo from my side .. thanks for correcting it 🙂

u sure ur annuity 1st eg is correct ??

im getting arnd 33.6 lac..??

@Rahul,

I agree with you, it comes to ~33.6 lacs.

Looks like he has missed to substract 1 from (1+.015)^120, that way it comes to ~40.39 lacs.

@Jagoinvestor,

can you please correct the calculation mistake if I am not wrong.

@KAMAL and @Rahul

You guys are correct . I am wrong 😉 .

I forgot to subtract 1 i guess ..

Manish

Compound interest formula is : A = P * (1+r/n)^(nt) and not A = P * (1+r/t)^(nt).

Typo ?