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!
Sorry. I missed this in my previous comment.
There N=(1+(r/n))^(n/12)
Where n = no. of time interest is compounded per year (4 for quaterly)
And r= rate of interest as a decimal (0.08 for 8%)
Hi,
I just found a formula for calculating the final amount using the logic provided here and thought this will be useful for you all.
A=P(1-(N^(m+1)))/(1-N) – P
May be the admin can post the formula in a more readable form. 🙂
Cheers!!!!
How to exactly calculate Int on Recurring Deposit?
If i make biweekly deposits of $135 and the interest compounds biweekly at the rate of .8% for 15 years, how much money will I have at the end of the 15 years
Thanks
I have $135 bi weekly deposits compounded bi weekly at .8%, how much money will there be in 15 years? Can you please explain how you did it too.
Thanks
Hi,
I have used the mentioned formula for RD calculation (Future Value) and the result also in line with the method of calculating of RD by Banks (ref: http://www.allbankingsolutions.com/Recurring-Deposit-Calculator-India.shtml) with quarterly compounding effect. But the results are in line up to 3 years (time frame), while calculating more than 3 years terms it is not matching with the result of banks.
Please let me know how could I address the issue.
I found this is really useful and I must thank you for your efforts. Can you also share a similar table for FDs. It will be really helpful.
thank you
Thanx. Its really very helpful. The calculations are exact.
Hi Manshu,
Thanks for such a simplified explanation.
I was wondering if we can use the future value of an Annuity formula to arrive at the maturity amount in the case of an RD. If yes, can u please eloborate the workings of the same.
Thanks in advance
Ankith
Yes Ankith, you should be able to do that by simply multiplying time periods by 12 and dividing interest rate by 12 in the standard formula. Did you try that? I think that’s all you’d need to do.
Yea I did try it out. I think multiplying and dividing by 12 would work only when the interest is compounded monthly. As you know many of the banks compound the interest on a quarterly basis. Lets say for example I invest INR 2000 per month for the next 24 months and if i calculate in excel as expalined by you, the maturity amount would be INR 53148(Interest rate being 9.75% compounded quarterly) and when I consider the future value formula, the maturity amount would be INR 50310(after dividing the interest rate by 24 and multiplying the time period by 24).
Is there a way to use the future value of annuity formula when the interest is compounded quarterly and also supposing I pay the RD amount at the beginning of every month, shouldn’t it be considered as annuity due and not as ordinary annuity? In either case I am not getting the value that matches with the working suggested by you. Please do clarify this ambiguity.
Thanks in advance
Another interesting point, though it hasn’t discussed in this forum, is about taxability of interest from RD. Unlike other fin’l products, interest in RD a/c is taxable on annual basis, not on maturity. Bank / PO doesn’t deduct TDS or gives exemption. Hence, the net return should be calculated depending upon which tax bracket an investor is.
Sir I m depositing 25000 every month in RD I have to deposit for 10 years So pl.let me know the interest I will get every year for income tax purpose. Interest is calculated monthly.
Thanks Mukesh
Dear Mukesh,
Interest is calculated monthly but paid in the account after the quarter. Now for interest calculation, I will give you logic and then you can calculate ineterest for n years yourself.
In RD, interest on any months’ deposit is calculated on the basis of no. of months eligible for ineterest credit as on interest date. Now let’s take our Rs. 2,000 gets deposited on 1st Jan, 1st Feb and 1st Mar. Since interest will be calculated after this quarter, the calculations will be as following:
1. Interest on Jan deposit = 2,000 x 3 months (Jan till Mar) x 8.6%/12 (monthly interest)
= 43
2. Similarly, interest on Feb deposit = 2,000 x 2 months (Feb and Mar) x 8.6%/12 = 28.67
3. and interest on Mar deposit = 2,000 x 1 month (Mar) x 8.6%/12 = 14.33
Total accumulated interest = Rs. 86
Similarly, interest will be calculated after 2nd quarter i.e. Jan deposit will get interest for 6 months + Feb deposit for 5 months + ……..+ Jun deposit for 1 month = 301. This is total accumulated interest till end of 2nd quarter. But since interest (86) at end of quarter 1 was paid already, 301 – 86 = 215 will be paid as interest in the account at quarter 2.
Hope it helps.
what is months expressed in an year? how is that calculated?
also, will this calculation help with different installments.
Basically i paid off a loan borrowed from my mom, amounts vary in a month.
I have paid off the principle. Need to calculate interest at 8% p a, compunded monthly.
please help.
Interest on loan repayment is calculated on reducing principal basis. You need to calculate due interest on due loan amount at end of every month. For compound benefit, you need to add up this interest in the due loan amount as opening balance of next month. Once payment is done, due loan amount gets reduced by paid amount and interest is calculate on balance due amount. Let me make it clear nby this example:
Let’s assume you borrowed Rs. 10,000 from your mom on 1st Jan to return within 1 year at 8% p.a. compounded monthly. I will explain reduced principal basis with 3 scenarios:
1. Simple interest: Had you paid SI, your interest payble at year end will be = 10,000 x 8% = 800 (no brainer !)
2. Compounded intrest: In logical terms, it can be calculated for 12 months as following:
Opening Balance Monthly interest Closing balance
10,000 67 10,067
10,067 67 10,134
10,134 68 10,201
10,201 68 10,269
10,269 68 10,338
10,338 69 10,407
10,407 69 10,476
10,476 70 10,546
10,546 70 10,616
10,616 71 10,687
10,687 71 10,758
10,758 72 10,830
Hence, Compound interest is 10830-10000 = 830
Also, In mathematical terms it will be 10,000 x (1+8%/12)^12 – 10000 = 830
3. Now comes Reducing principal…..Let’s assume you returned 2000 in feb, 3000 in May, 2000 in Oct and balance 3000 in Dec. I am making it not only varying amount but also irregularly paid in tranches. Let’ look at interest payble at year end:
Month Opening Balance Monthly interest Princi paid Closing balance
Jan 10,000 67 10,067
Feb 10,067 67 2000 8,134
Mar 8,134 54 8,188
Apr 8,188 55 8,243
May 8,243 55 3000 5,298
Jun 5,298 35 5,333
Jul 5,333 36 5,368
Aug 5,368 36 5,404
Sep 5,404 36 5,440
Oct 5,440 36 2000 3,476
Nov 3,476 23 3,500
Dec 3,500 23 3000 523
Hope this helps.
when the deposit for the 24th month is held for one more month for maturity, then the first deposit, the interest should be for 25 months and similar for other deposits??
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.
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 🙂
Excellent – congrats!
Please tell me the formula used to calculate RD.
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.
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.
The calculator at PPF calculator might be of help!