Pradeep Sharma left a comment the other day about how he had set up a recurring deposit with ICICI Bank and how the final amount he was calculating was different from the amount that the ICICI Bank representative told him.

That difference was due to the fact that while he was compounding interest monthly, banks usually compound interest quarterly and that’s why he was getting a different answer.

Paresh responded to that comment telling him what caused the difference, and when I looked at the response, I thought I’d add to it by providing a link to how interest on recurring deposits (RDs) are calculated.

I was surprised to see that while there were quite a few recurring deposit calculators, there were hardly any explanations and the few that existed were really very short explanations on how interest on RD was calculated.

So, I decided to give it a try myself, and it took me an embarrassingly long time and several mistakes to do that even though the concept is very simple.

## Understand Compound Interest To Understand Recurring Deposit Interest

When you create a RD for Rs. 10,000 for 2 years, what you’re doing is depositing Rs. 10,000 with the bank every month for 24 months, and the bank pays you interest on Rs. 10,000 for 2 years compounding it quarterly, then for the next Rs. 10,000 it pays you interest for 23 months, and so on and so forth.

Banks usually compound interest quarterly, so the first thing is to look at the formula for compound interest.

That formula is as follows:

A formula for calculating annual compound interest is

Where,

- A = final amount
- P = principal amount (initial investment)
- r = annual nominal interest rate (as a decimal, not in percentage)
- n = number of times the interest is compounded per year
- t = number of years

In your recurring deposit, you use this formula to calculate the final amount with each installment, and at the end of the installments, you add them all up to get the final amount.

## Think of RD Installments and Series of Principal Payments

Let’s take a simple example to understand this – suppose you start a recurring deposit for Rs. 47,000 per month for 2 years at 8.25% compounded quarterly. If you were to see this number as a standalone fixed deposit that you set up every month for 24 months, you could come up with a table like I have here. Before you get to the table, here is a brief explanation on the columns.

**Month:**First column is simply the Month.**Principal (P):**Second column is P or principal investment which is going to be the same for 24 months,**Rate of Interest (r)**: r is going to 8.25% divided by 100.**1+r/n:**In our case, n is 4 since the interest is compounded quarterly, and 1+r/n is rate divided by compounding periods.**Months Remaining**: This is simply how far away from 2 years you are because that’s how much time your money will grow for.**Months expressed in year:**I’ve created a column for Months expressed in a year since that makes it easy to do the calculation in Excel.**nt:**4 multiplied by how many months are remaining as expressed in year.**(1+r/n)^nt**: Rate of interest raised by the compounding factor.**Amount (A)**: Finally, this is the amount you if you plug in the numbers in a row in the compound interest formula.

So, Rs. 47000 compounded quarterly for 2 years at 8.25% will yield Rs. 55,338.51 after two years. The last row contains the grand total which is what the RD will yield at the end of the time period.

Month |
P |
r |
1+r/n |
Months remaining |
Months expressed in year |
nt |
(1+r/n)^nt |
A |

1 |
47000 |
0.0825 |
1.020625 |
24 |
2 |
8.00 |
1.18 |
55338.51 |

2 |
47000 |
0.0825 |
1.020625 |
23 |
1.916666667 |
7.67 |
1.17 |
54963.21 |

3 |
47000 |
0.0825 |
1.020625 |
22 |
1.833333333 |
7.33 |
1.16 |
54590.45 |

4 |
47000 |
0.0825 |
1.020625 |
21 |
1.75 |
7.00 |
1.15 |
54220.22 |

5 |
47000 |
0.0825 |
1.020625 |
20 |
1.666666667 |
6.67 |
1.15 |
53852.50 |

6 |
47000 |
0.0825 |
1.020625 |
19 |
1.583333333 |
6.33 |
1.14 |
53487.27 |

7 |
47000 |
0.0825 |
1.020625 |
18 |
1.5 |
6.00 |
1.13 |
53124.53 |

8 |
47000 |
0.0825 |
1.020625 |
17 |
1.416666667 |
5.67 |
1.12 |
52764.24 |

9 |
47000 |
0.0825 |
1.020625 |
16 |
1.333333333 |
5.33 |
1.12 |
52406.39 |

10 |
47000 |
0.0825 |
1.020625 |
15 |
1.25 |
5.00 |
1.11 |
52050.97 |

11 |
47000 |
0.0825 |
1.020625 |
14 |
1.166666667 |
4.67 |
1.10 |
51697.97 |

12 |
47000 |
0.0825 |
1.020625 |
13 |
1.083333333 |
4.33 |
1.09 |
51347.35 |

13 |
47000 |
0.0825 |
1.020625 |
12 |
1 |
4.00 |
1.09 |
50999.12 |

14 |
47000 |
0.0825 |
1.020625 |
11 |
0.916666667 |
3.67 |
1.08 |
50653.24 |

15 |
47000 |
0.0825 |
1.020625 |
10 |
0.833333333 |
3.33 |
1.07 |
50309.72 |

16 |
47000 |
0.0825 |
1.020625 |
9 |
0.75 |
3.00 |
1.06 |
49968.52 |

17 |
47000 |
0.0825 |
1.020625 |
8 |
0.666666667 |
2.67 |
1.06 |
49629.63 |

18 |
47000 |
0.0825 |
1.020625 |
7 |
0.583333333 |
2.33 |
1.05 |
49293.05 |

19 |
47000 |
0.0825 |
1.020625 |
6 |
0.5 |
2.00 |
1.04 |
48958.74 |

20 |
47000 |
0.0825 |
1.020625 |
5 |
0.416666667 |
1.67 |
1.03 |
48626.71 |

21 |
47000 |
0.0825 |
1.020625 |
4 |
0.333333333 |
1.33 |
1.03 |
48296.92 |

22 |
47000 |
0.0825 |
1.020625 |
3 |
0.25 |
1.00 |
1.02 |
47969.38 |

23 |
47000 |
0.0825 |
1.020625 |
2 |
0.166666667 |
0.67 |
1.01 |
47644.05 |

24 |
47000 |
0.0825 |
1.020625 |
1 |
0.083333333 |
0.33 |
1.01 |
47320.93 |

Final Amount |
12,29,514 |

I’ll be the first one to admit that this is not a very intuitive way to either explain or understand recurring deposits calculation, but this is the only way I could write which seemed to convey the calculation comprehensively.

If you have any questions or have links to better ways to explain this then please leave a comment!

{ 60 comments… read them below or add one }

Thanks a lot – you saved me lot of work!

There is not much data available on the formula for calculating recurring post.

You are a saviour. I was procarstinating about doing this calculation from so long. π Thanks π

I should have created a Google Spreadsheet or something and that would have made your life a bit simpler too!

A spreadsheet [XLS] that’s downloadable would be super helpful for lazibones like me! π

The link to the calculator is far more useful than my excel since that calculator gives you the number ready, and in my sheet you have to make a lot of changes if your term is different, compounding is different etc.

Worth reading, analyzing and making others aware:

http://ftalphaville.ft.com/blog/2012/03/30/944431/indias-economic-monsoon/

Absolutely right Ankur – I have a post in my drafts about this as soon as the report came out but didn’t publish it yet because I’m simplifying it and adding more data, but I will definitely link to this article in my weekend post. Thanks for leaving this comment here and bringing it up.

Oops!!! My apologies – Ankush!

thanks a lot for this article, it would be great if you include the tax implication of the same.

Prashant,

The interest earned through RD will be included in your income and will be taxed. There is no tax exemption for RD.

Manshu, thanks for the good post.

Thanks for the response Vimal – the one thing I’ve heard differing opinions on is when should the tax be paid. Should it be paid every year since the income is accruing every year (even though it’s not getting paid) or should it be paid at the end of the RD term when the person actually gets the money. What are your thoughts?

Thanks!

When it comes to paying taxes on the interest earned there always is this question whether to pay it on per year basis or directly on maturity. The point here to be noted is that when you pay on a per year basis you end up paying a small tax amount only on the interest earned during that particular year, whereas when you think of paying it on maturity you may end up paying some more tax because the whole interest amount accrued over the period would add to your annual income and may end up moving your taxable income in the next higher tax slab and that really makes a good difference when the interest amount is higher, just consider for eg. you earn a total of 25K as only interest may be the same is from KVP / NSC / FD / RD.

Thanks for the point Rupesh – so the laws allow you to choose which one to do? pay tax now or pay tax later? That’s what I’m not so clear about whether both are okay or not, people have said that they have chosen either option but I’m not sure whether there is any official guidance on this.

It is a sum of a Geometric Progression (GP).

I use this formula for monthly deposits.

P=monthly installment, r = rate %, y=no.of years, n=12*y, R=1+(r/1200)

A= P*(R)*(R^n-1)/(R-1)

For derivation, look at your +1 Maths book

Thanks – I need to look this up and I must admit it didn’t occur to me at all to use GP. Thanks for bringing this up.

Nice post Manshu.

Thanks!

Thanks for the info which gave a different approach…..RD from the point of view of FD….it was helpful. And i like your eagerness to make people understand in a easy way.

Thanks Ramya – this was certainly one way, but perhaps doing it through geometric progressions as said in comments is better. I will have to look at that and see if this can be further simplified.

Manshu,

I also think that this logic [considering the individual installment as Fd / calculating the interest for a period for each deposit/ sum it up] is not a true representation of recurring deposit..

I have one RD at IDBI bank with interest rate of 8.6% ..just I check the deposit schedule which I found for first few installments as below:

Payment Type Date Amount Paid Balance

Installment 03/01/2011 2000/- 2000/-

Installment 03/02/2011 2000/- 4000/-

Installment 03/03/2011 2000/- 6000/-

Installment 03/04/2011 2000/- 8000/-

INTEREST 03/04/2011 86 /- 8086/-

Installment 03/05/2011 2000/- 10,086/-

Installment 03/06/2011 2000/- 12,086/-

Installment 03/07/2011 2000/- 14,086/-

INTEREST 03/07/2011 216/- 14302/-

Installment 03/08 2000/- 16302/-

AND SO ON………………

I tried few things for my blog but not able to fit any formula …..

just check,, I think you will be….

Just for more elaboration:

In above deposit schedule,I just fail to understand how interest of Rs.86 credited on 03/04/2011 or Rs 216/- credited on 03/07/2011…..

My feeling is that there is something which is on the shorter sight only but not able to find…..

You didn’t mention why you think that way Paresh – is it just a feeling or something more than that? I’m convinced that this is accurate and don’t feel compelled to relook at it unless you can give some numbers or something else more concrete to show it’s inaccurate.

Ohhh,please don’t misunderstood me…really sorry if you feel bad..

I have never mean that you are inaccurate….

I have tried to present the numbers from my IDBI RD account…where I do not understand the logic that how they calculate the interest flow….thats what I was looking for.

No, no, no, I didn’t misunderstand or feel bad and you certainly don’t need to say sorry but I was asking more in terms of what I should look for if I have to see whether there is an error or not. I didn’t realize that the RD numbers were for that purpose alone. I’ll look at the RD numbers.

Sorry for the miscommunication.

Thanks for that.

What I was looking for is actually available in your post and work ….

Just able to solve the calculation of deposit schedule.

Have tried a deposit schedule for above particular case also:

Payment Type– Rs.——– A/C.Balance

1)Principle——>47000 —— 47000

2)Principle——>47000——- 94000

3)Principle——>47000——- 141000

4)Principle——>47000——–188000

5)INTEREST——- 3231.28——191231.28

6)Principle——>47000——–238231.28.

7)Principle——>47000 ——-285231.28

8)Principle——->47000——-332231.28.

9)INTEREST——–5878.50—–338109.78

10)Principle—–>47000——-385109.78

11)Principle—–>47000——-432109.78

12)Principle—–>47000——-479109.78

13)INTEREST—— 8907.87—–4,88017.65

14)Principle—–>47000——-535017.65

15)Principle—–>47000——-582017.65

16)Principle—–>47000——-629017.65

17)INTEREST—— 11999.71—-641017.36

18)Principle—–>47000——-688017.36

19)Principle—–>47000——-735017.36

20)Principle—–>47000——-782017.36

21)INTEREST——-15155.33—-797172.69

22)Principle—–>47000——-844172.69

23)Principle—–>47000——-891172.69

24)Principle—–>47000——-938172.69

25)INTEREST——-18376.04—-956548.73

26)Principle—–>47000——-1003548.73

27)Principle—–>47000——-1050548.73

28)Principle—–>47000——-1097548.73

29)INTEREST——-21663.17—-1119211.90

30)Principle—–>47000——-1166211.90

31)Principle—–>47000——-1213211.90

32)INTEREST——-16301.72—-1229513.62

Please do not get confused with serial Number.

Serial number 32 is a flow serial number…do not represent the number of month…

Date of interest addition and installment on that date will be same..Total period is 24 months.

Hi Paresh, how did you calculate Interest at every interval?

Its quite a simple riddle:

Actually on 03/01/2011: Your final amount was 2000

And on 03/02/2011: Your final amount was 2000+2000=4000

And on 03/03/2011: Your final amount was 6086(With Interest)

And on 03/04/2011: Your final amount was 6086+2000=8086

And on 03/05/2011: Your final amount was 8086+2000=10086

And on 03/06/2011: Your final amount was 10086+2000=12302(With Interest)

And on 03/07/2011: Your final amount was 12302+2000=14302

And on 03/08/2011: Your final amount was 14302+2000=16302

And so on..

Hopefully,you got what i wanna convey.. everything is right but you or the authorities just misplaced the dates/entries in the final statement..

Any doubts,will be happy to clear it..!!

Hi,

Really greatful for your detailed & precise explaination…I was brainstorming on the calculation along with my frens since yesterday & could find no way of reaching the correct answer.

Your hard work has made me happy & got to learn a lot of things in the course of trial & error.

Kudos to u & ur effort..keep up the good work.

Thanks π

Is RD interest taxable? Do reply me soon π

I wish to ask the same question you can reply me on either of the 2 IDs !!!

Is RD interest taxable ? Do reply me soon

Yes, Fully Taxable. Interest accrued from RD / FD adds to the annual income & an individual is liable to pay tax on the same.

There is a simple formula for calculating future value (accumulated amount) of a recurring deposit:

FV = A *{[ (1+i)^n] -1}/i

FV = future value

A = Recurring deposit amount

i= interest rate

n = period

sir, my question is how to calculate the interest if i am depositing money annually.

like i pay my premiums to the life insurance company annually 10000. so say after 10 years how can i calculate the interest. let rate of interest be according to the market rates.

please explain the process n the formula.

Here is a good post that explains how to do this with a video tutorial, I think this post will answer all your questions.

http://www.jagoinvestor.com/2011/02/calculate-insurance-policies-returns-video.html

thanks sir.. clear concept

One subtle point is that it is important to know which 2 years the deposit is taken on. That is, the date of deposit could alter the final amount a little bit. For example, a 2-year deposit taken on 1-Feb-2012 will end on 1-Feb-2014 and will have a total of 731 days (2012 being a leap year) for which interest will have to be accrued, whereas a 2-year deposit taken on 1-Feb-2013 ending on 1-Feb-2015 will accrue interest on 730 days only.

In essence, the payment frequency a.k.a number of days between each actual payment period (monthly in your example) will determine the interest amount for that period and the sum of all those amounts for the tenure will yield the final deposit amount.

Thanks for bringing that up BV.

i’ll get rs 1.44 lacs by investing rs 1500 p.m for 5yrs.i would like to know what is the interest i am getting?and i dnt knw how many times interest is compounding in a year u can assume once in a year.

interest i mean rate of interest.

Around 18%.

Can u please explain hw u calc ? Any Formula ?

thanks.

Hi Manshu,

Nice post!

I did lots of r&d to achieve this but unfortunately i couldn’t make it. You save lots of my time. Really appreciate your hard work.

Even I was looking Fixed Deposits. I am not sure whether we already have it. Pls let me know your view if possible.

Thx,

Satya

Guys can you help me out with a formula for PPF where i would be depositing Rs 50000 on anually basis for 15 years what would be amount at maturity…. Calculated manually but if you guys can help me out with formulla that would be a real help….

The calculator at PPF calculator might be of help!

Hi Manshu,

I am a regular reader of your blog and subscribe through google reader. I have recently opened a RD in icicibank.com and I’d like to show you how the bank is cheating/earning interest while we fail to earn interest.

Step1: Click on Open a fixed deposit/recurring deposit

Step2: Open the RD form. You’ll notice a form very similar to this:

https://dl.dropbox.com/u/34070124/iciciRD.jpg

I have highlighted the most important note10. I had opened the RD on 28th September and chose the date as 1st of every month.

Now, this is what happens. The first installment was debited on 28th and the second one was debited on 1st of October. But, the money debited from my savings account for the second installment was not credited into my RD. I think it would be credited on 28th.

I checked my RD account and it shows the maturity date as 28th June 2013 and checked the amount. The amount and the date are correct. But, what is really happening here is that the amount which is debited on 1st does not fetch any interest until 28th of every month, which essentially means almost one entire month.

I could have chosen a better way, that is the date on which I am opening the RD as the date to debit the account from.

I felt completely cheated by this option. This date option is just like locking the amount until 28th and then putting in RD. This is how bank earns money in the garb of saving money for us.

I requested ICICI bank to change this option and emailed them. Let’s see. I felt this comment would be useful for a lot of readers.

In a completely unrelated note, a suggestion from my end, it will be great if you have this discussion or comments secion from http://disqus.com/ . I am not a salesperson of disqus.com, but this will help readers like me to check whatever comments I’ve made so far.

Wow! I had no idea about this! So when you contacted ICICI, they agreed that this is what was happening? It’s unbelievable! I think I’ll make this as a mini post and let others know that this is happening instead of this just being buried in comments.

Thanks a lot for sharing this.

I have once passed over Disqus because I felt that it will make OneMint dependent on availability of Disqus and I wasn’t sure if it is wise to rely on that. I think now it seems like it is fine to rely on their availability. I wish I knew how they make money…that always makes the decision easier. Thanks for the suggestion.

I am following up with ICICI bank. I’m not sure they have accepted it yet. But, I don’t think there’s any calculation mistake in my part. I have clearly put up in blogpost :

http://itooblog.wordpress.com/2012/10/04/investing-in-recurring-deposit/

I have emailed the customer care and am waiting for their reply.

After reading your blog post I understand this a little better, and realize that this happened only once at the setup. Correct?

This wasn’t clear to me earlier, it seemed like it was happening every month.

Since the amount is being debited from my savings account for every month, I should be getting interest for that. This is not one-time interest, every month I should be getting the interest. You could check out my 2nd table in the post.

But, the interest calculation is not correct. It could also be that recurring deposit calculates only based on months, the interest calculation does not consider any days.

I would like to confirm that from ICICI bank.

Hi Manshu,

I have created a blogpost out of my experience. You can check it here:

http://itooblog.wordpress.com/2012/10/04/investing-in-recurring-deposit/

Thanks.

Please tell me the formula used to calculate RD.

Hi,

Can u put the formula for one year

RD calculated annually

That is just the future value of an annuity, you can look up that formula to see how that works, but RDs are never annual. The payment is always monthly.

Thanks Manshu,

Yeah.. I know

Actually was looking for the formula to put it in my recurring deposit calculator code. I worked on it and did π

Excellent – congrats!

Thank you Manshu for explaining it so elaborately. It helped me to understand the concept of recurring deposits.

Thanks Manshu for explaining it so elaborately. Earlier I could not understand the concept from any website.