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!
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….
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
thanks.
interest i mean rate of interest.
Around 18%.
Can u please explain hw u calc ? Any Formula ?
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.
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.
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
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
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.
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,RD interest is taxable like FDR interest.
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 🙂
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..!!
Dear Paresh bhai,
Here is an attempt from myside to decode the RD interest piece. Here are basic premises:
1. The bank makes 2 entries in every 4th month i.e. interest for previous 3 months and monthly deposit of 4th month’s principal.
2. The interest concept can be simply understood in this way:
Interest as of any particular month will be simple interest accumulated on an amount till that month. Hence, in April’11, Jan’11 deposit will fetch interest for 3 months, FEb’13 deposit for 2 months and Mar’13 for 1 month. Together, this interest can be calculated as AP of 3+2+1 i.e.. (n*(n+1)/2)
3. Bank however credits this interest in 4thh month in line with concept explained by Manesh bhai. However, fresh interest credited in every 4th month is total interest accumulated on all principals of every month minus interest already credited to account holder.
4. I hv mentioned entry no. to bring clarity to all.
Entry No. Date of transaction Month count Deposited Money Balance Interest due till date Interest being credited account Balance
1 3-Jan-11 1 2000 2000 2000
2 3-Feb-11 2 2000 4000 4000
3 3-Mar-11 3 2000 6000 6000
4 3-Apr-11 3 86 86 6086
5 3-Apr-11 4 2000 8000 8086
6 3-May-11 5 2000 10000 10086
7 3-Jun-11 6 2000 12000 12086
8 3-Jul-11 6 301 215 12301
9 3-Jul-11 7 2000 14000 14301
10 3-Aug-11 8 2000 16000 16301
11 3-Sep-11 9 2000 18000 18301
12 3-Oct-11 9 645 344 18645
13 3-Oct-11 10 2000 20000 20645
14 3-Nov-11 11 2000 22000 22645
15 3-Dec-11 12 2000 24000 24645
16 3-Jan-12 13 1118 473 25118
17 3-Jan-12 13 2000 26000 27118
18 3-Feb-12 14 2000 24000 29118
19 3-Mar-12 15 2000 28000 31118
20 3-Apr-12 16 1720 602 31720
21 3-Apr-12 16 2000 30000 33720
22 3-May-12 17 2000 26000 35720
23 3-Jun-12 18 2000 32000 37720
24 3-Jul-12 19 2451 731 38451
25 3-Jul-12 19 2000 34000 40451
26 3-Aug-12 20 2000 28000 42451
27 3-Sep-12 21 2000 36000 44451
28 3-Oct-12 22 3311 860 45311
29 3-Oct-12 22 2000 38000 47311
30 3-Nov-12 23 2000 30000 49311
31 3-Dec-12 24 2000 40000 51311
32 3-Jan-13 25 4300 989 52300
Hope this helps.
what is the percentage that you have taken ? could u please tell if you dont mind and give the illustration for the first three month i mean the working thank you…
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.
Nice post Manshu.
Thanks!
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.
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.
I guess there isn’t a choice that you could make to pay on a y-o-y basis or on cumulative int. earned for the period. The Bank that holds your RD would certainly book the interest earned by you during an FY (without paying you) and include it as part of their interest payouts and that eventually gets reflected in your 26AS. This also gets reflected in the Interest paid statement that the bank gives you for each FY.
So it is always…….interest earned during an FY is included in the total income for the FY from tax purposes irrespective of the length of the investment.
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!
You are a saviour. I was procarstinating about doing this calculation from so long. 🙂 Thanks 🙂
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! 😉
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.
You can download it from here- http://interestcalculations.blogspot.com/
Thanks a lot – you saved me lot of work!
There is not much data available on the formula for calculating recurring post.
Naresh deposited rp 2000 at the beginning of every month in a bank for 5 year.the rate of interest is 12? compounded monthly. The accumulated amount at the end of 5 years will be?
Actually answer is 164973 I have want to know the method of calculate, pls help me to resolve
How to calculate RD account
for calculating RD 1 formula is there
MV= Pn+Pn(n+1)RT/2×100
for T the value is fixed T=1/12
now the formula will be,
MV=Pn+Pn(n+1)R×1/2×100×12
You have to find only the missing term
e.g.
Anil opened aRD account in a bank and diposited Rs.400 per month for 3 years if he recevied Rs.15732 at the time of maturity find the rate of intrest per annum.
MV=Rs.15732(its written recivied or get)
P=Rs.400
n=3years
=3×12
=36(n will be always in months)
R= the missing term
now putting the formula
=MV=Pn+Pn(n+1)R×1/2×100×12
=15732=400×36+37×R×1/2×100×12
=by solving we get,
=15732=14400+222R
Moving the R to LHS we get,
=222R= 15732-14400
222R=1332
R=1332/222
R=6 .ans
The Rate of interest will be 6%
A recurring deposit of Rs. 5000 per month for 12 installments will grow to ______ at the
end of 12 months for the given nominal interest rate of 12 percent, but compounded
monthly (consider deposit being done on the last day of the month and also accrual of
interest being calculated on the last day of the month).
How do calculate Recurring deposit?
Please provide the formula and explain
Example: Each month Paying 4200 in 1year and interest rate 6.85 %
I have monthly deposite 500 in recuring account 8% intrest
How many get intrest amount
How caculate
Naresh deposited rp 2000 at the beginning of every month in a bank for 5 year.the rate of interest is 12? compounded monthly. The accumulated amount at the end of 5 years will be?
Actually answer is 164973,
I want to know the method of calculation, pls help me to resolve
i am much impressed by the answer and the method i.e formula
Mr.A invested Rs.400000 in post office MIS and the proceedings from this investment is directly transferred to post office RD. How much amount will he get after maturity?
Please mail the formula for calculating interest on Recurring deposit on quarterly compounding method as being practice in banks.
@bemoneyaware: Here is the formula to calculate-
http://interestcalculations.blogspot.com/2016/08/formula-for-total-maturity-amount-with.html
And here is how it’s calculated-
http://interestcalculations.blogspot.com/2016/08/deriving-formula-for-total-maturity.html