Calculating Accrued Interest of a Bond

gcefaloni

Board Regular
Joined
Mar 15, 2016
Messages
117
Hi,

I'm trying to calculate accrued interest since last coupon payment date (using ACCRINT function) without any helper columns. I have access to Issue date, first coupon, coupon rate, coupon frequency, par amount and every information needed for the ACCRINT function to work.

So, essentially I have daily dates rolling down (in column A), and interest accrued in a bond payment (in Column B) up until the actual coupon is paid out at which date the accrued interest needs to come back to zero. The following day after a coupon payment, interest accrued needs to restart accumulating in column B. So on and so forth. Accrued interest accumulates until the coupon payment is made, at which date it goes to 0. Rinse and repeat.

The problem I'm having is that I don't know how to make it recognize when the coupon payment date is and then have the following accrued interest calculation take that date as the new last coupon date. All that without using a helper column.

DB - Historical CAN Bond Data - Interest accrued.xlsb
AB
1INT_ACC01285PBU1
2SECURITY_NAMEALBCAP 4.45 12/15/25
3ISSUE_DT10/5/2005
4FIRST_CPN_DT12/15/2005
5CPN4.45
6CPN_FREQ2
7PAR_AMT5000
Sheet1


I'm on my way there but not quite. I'm not sure I'm going the right way about this. Right now, the accrued interest just keeps accumulating from the issue date and never resets back to 0 when a coupon is supposed to be paid (every 6 months).

DB - Historical CAN Bond Data - Interest accrued.xlsb
AB
24749/30/2005 
247510/1/2005 
247610/2/2005 
247710/3/2005 
247810/4/2005 
247910/5/20050
248010/6/20050.618056
248110/7/20051.236111
248210/8/20051.854167
248310/9/20052.472222
248410/10/20053.090278
248510/11/20053.708333
248610/12/20054.326389
248710/13/20054.944444
248810/14/20055.5625
Sheet1


Any help on how to make the column B reset to 0 when an interest payment is made (6 months from the last coupon payment date) and the restart calculating from that new last coupon date, would be EXTREMELY appreciated.

Initially, that was my first formula: =IF(A2480=DATEVALUE(B$3),0,IF(A2480<DATEVALUE(B$3),"",ACCRINT(B$3,B$4,A2480,B$5/100,B$7,B$6,0,FALSE)))
But then I needed to find a way to make the last coupon payment date change so I tried to add this: INDEX($A$1:$A2479,AGGREGATE(14,6,ROW($B$1:$B2479)/($B$1:$B2479=0)*($B$1:$B2479<>""),COUNTIF($B$1:B2479,0))) but I still don't know how to make the cell change to 0 when a coupon is paid...

I'm confused at this point and need help sorting this out.

Again, any help would be very very appreciated.

Thanks!
I posted the same question on: Calculating accrued interest
 
Last edited by a moderator:

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KRice

Well-known Member
Joined
Dec 9, 2003
Messages
1,061
Office Version
  1. 2019
Platform
  1. Windows
Don't most bonds pay a simple interest rate? If so, then an approach like this might give you the results you want. This computes the daily accrual only once, and since that is a fixed amount, it is placed at the top of the date range and referenced when called for.
Book2
AB
1INT_ACC01285PBU1
2SECURITY_NAME
3ISSUE_DT10/5/2005
4FIRST_CPN_DT12/15/2005
5CPN4.45
6CPN_FREQ2
7PAR_AMT5000
8Maturity (y)2
9Daily Accrual0.618055556
10
11
129/30/2005 
1310/1/2005 
1410/2/2005 
1510/3/2005 
1610/4/2005 
1710/5/20050
1810/6/20050.618055556
1910/7/20051.236111111
2010/8/20051.854166667
2110/9/20052.472222222
2210/10/20053.090277778
2310/11/20053.708333333
2410/12/20054.326388889
2510/13/20054.944444444
2610/14/20055.5625
1954/1/2006110.0138889
1964/2/2006110.6319444
1974/3/2006111.25
1984/4/2006111.8680556
1994/5/20060
2004/6/20060.618055556
2014/7/20061.236111111
37810/1/2006110.6319444
37910/2/2006111.25
38010/3/2006111.8680556
38110/4/2006112.4861111
38210/5/20060
38310/6/20060.618055556
38410/7/20061.236111111
38510/8/20061.854166667
38610/9/20062.472222222
38710/10/20063.090277778
Sheet1
Cell Formulas
RangeFormula
B9B9=ACCRINT(B$3,B$4,B3+1,B$5/100,B$7,B$6,0,FALSE)
B378:B387,B195:B201,B12:B26B12=IF(AND($A12>=$B$3,$A12<=EDATE($B$3,$B$8*12)),IF(AND(MOD(MONTH($A12)-MONTH($B$3),12/$B$6)=0,DAY($B$3)=DAY($A12)),0,B11+$B$9),"")

I've hidden a lot of intermediate rows to show the reset to 0. Note that this also adds a maturity date to the top bit of information so that the formula can return a 0 once the maturity is reached. I don't quite understand the relationship between the issue date and the 1st coupon date, so the formula might be correct in that it begins when desired, or that might need to be tuned further. This also assumes that the reset date corresponds to the same day of the month as the starting "0", meaning that a "month" interval consists of variable days depending on which particular months are involved.
 

KRice

Well-known Member
Joined
Dec 9, 2003
Messages
1,061
Office Version
  1. 2019
Platform
  1. Windows
I think the formula I posted may need some adjustment. Please have a look at the initial "0" date and then evaluate what happens at the end of the payment interval. The last day of accrual for any given period should represent both the cumulative payment that you want during that 6-month period AND a reset to 0 on that same day so that the next day's accrual is accounted for. The current formula sets the next day's accrual to 0, which I believe is incorrect. By the way, if interest is indeed simple interest, then it really isn't necessary to document daily accruals. A much shorter table could be developed to describe only the beginning and end dates of the payment periods, and then describe the cumulative interest during that period...but that may not be what you have in mind.
 

gcefaloni

Board Regular
Joined
Mar 15, 2016
Messages
117
I think the formula I posted may need some adjustment. Please have a look at the initial "0" date and then evaluate what happens at the end of the payment interval. The last day of accrual for any given period should represent both the cumulative payment that you want during that 6-month period AND a reset to 0 on that same day so that the next day's accrual is accounted for. The current formula sets the next day's accrual to 0, which I believe is incorrect. By the way, if interest is indeed simple interest, then it really isn't necessary to document daily accruals. A much shorter table could be developed to describe only the beginning and end dates of the payment periods, and then describe the cumulative interest during that period...but that may not be what you have in mind.

Thank you KRice! It's very close but there are some small changes that need to be made. I'm not sure I understand fully what you were referring to in this above comment. I have attached some info with the correct information in column C. The column C doesn't change the accrued interest during weekends and then adjusts on mondays but that doesn't matter. I'm fine with the way we were doing it. The issue I'm having however is that you were starting the payments on the Issue date when in reality the first "0" happens on the first payment date (B4). The accrued interest starts accumulating on the issue date (B3) and then starts resetting every 6 months from the first payment date (B4). In the version that you had written, the 6 month cycles were happening from the issue date rather than the first payment date. In my version as attached below, it starts on the first payment date (B4) but it lacks the accumulated interest between the issue date (B3) and the first coupon payment date (B4). I need to adjust for that but not sure how to.

Here is the correct data in Column C, but I'm not sure where the differences come from. The Column C data between December 15th and June 15th adds up to 24.5298 and our calculated Column B adds up to 24.7469 which seems to be creating a bit more interest accrued than there should be.

I've also adjusted your B9 cell to: =ACCRINT(B$3,B$4,B3+1,B$5/100,B$7,B$6,0,FALSE)/B7*100 in order to adjust for the PAR_AMT. So that normalizes all bonds back to a par amount of 100.

DB - Historical CAN Bond Data - Interest accrued.xlsb
AB
3ISSUE_DT10/5/2005
4FIRST_CPN_DT12/15/2005
5CPN4.45
6CPN_FREQ2
7PAR_AMT5000
8MATURITY (Y)20
9DAILY_ACCRINT0.012361
Sheet1


DB - Historical CAN Bond Data - Interest accrued.xlsb
ABC
254112/4/2005 0.743699
254212/5/2005 0.743699
254312/6/2005 0.75589
254412/7/2005 0.768082
254512/8/2005 0.780274
254612/9/2005 0.792466
254712/10/2005 0.829041
254812/11/2005 0.829041
254912/12/2005 0.829041
255012/13/2005 0.841233
255112/14/2005 0.853425
255212/15/200500
255312/16/20050.0123610.012192
255412/17/20050.0247220.048767
255512/18/20050.0370830.048767
255612/19/20050.0494440.048767
255712/20/20050.0618060.060959
255812/21/20050.0741670.073151
255912/22/20050.0865280.085342
256012/23/20050.0988890.097534
256112/24/20050.111250.13411
256212/25/20050.1236110.13411
256312/26/20050.1359720.13411
27236/4/20062.113752.096986
27246/5/20062.1261112.096986
27256/6/20062.1384722.109178
27266/7/20062.1508332.12137
27276/8/20062.1631942.133562
27286/9/20062.1755562.145753
27296/10/20062.1879172.182329
27306/11/20062.2002782.182329
27316/12/20062.2126392.182329
27326/13/20062.2252.194521
27336/14/20062.2373612.206712
27346/15/200600
27356/16/20060.0123610.012192
27366/17/20060.0247220.048767
27376/18/20060.0370830.048767
27386/19/20060.0494440.048767
Sheet1


P.S. The reason why I need daily interest accrued is because I have the bond price movements over time on a daily basis but it does not include the accumulated interest from simple coupon payments. My end goal is to calculate total return for the bonds on a daily basis that would incorporate both price and interest accrued daily. In order to do that, I will add up the price for a given day and add up the accrued interest for that day and then compare it to the previous day's price and accrued interest in order to have a total return for that day. That is why I'm trying to accurately calculate interest accrued on a daily basis even if it is indeed a simple interest payment as you suggested.
 
Last edited:

KRice

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Joined
Dec 9, 2003
Messages
1,061
Office Version
  1. 2019
Platform
  1. Windows

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Thanks for the feedback and the explanations that have cleared up some points of confusion I had: one dealt with where the first "0" occurs, another dealt with whether there was some compelling reason for daily amounts. As for tweaking the formula, one concern I had relates to the transition from the end of one payment period to the next. I'll try to explain:
If the 1st coupon date is 12/15/2005 (the first "0"), then is the next coupon paid on 6/15/2006...or is it 6/14/2006? This is why I wonder whether a date condition needs to be tweaked by one day. And then is the day following a payment truly "0"? What happened to the accrual that should have accrued during that "0" day.

I think I understand the discrepancy between column B and column C. Have a look at any day following a "0" where we see one day's accrual. The clue here is that the constant daily accruals are different! The reason appear to be that Excel uses a 365-day year basis while column C uses a 360-day year basis.
0.0445/365 = 0.000121918 (consistent with column C)
0.0445/360 = 0.000123611 (consistent with column B ACCRINT formula)

If you'd prefer, the ACCRINT formula could be replaced with a standard daily rate using a 360-day year basis to maintain consistency with other data.

Let me know your thoughts on this and I'll have a look at the other accrual issue you mentioned to account for it.
 

KRice

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Joined
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Messages
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Office Version
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Platform
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I switched my 360/365 statements...col B uses a 360-day year (Excel's ACCRINT) while col C uses a 365-day year.
 

KRice

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Joined
Dec 9, 2003
Messages
1,061
Office Version
  1. 2019
Platform
  1. Windows

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There is a basis option in the ACCRINT function for using a 365-day year. Here is a revision with that option and a modified cumulative accrual formula that uses a series of IF statements to determine position on the calendar:
Book2
AB
1INT_ACC01285PBU1
2SECURITY_NAME
3ISSUE_DT10/5/2005
4FIRST_CPN_DT12/15/2005
5CPN4.45
6CPN_FREQ2
7PAR_AMT5000
8Maturity (y)20
9Daily Accrual0.012191781
Sheet1
Cell Formulas
RangeFormula
B9B9=ACCRINT(B$3,B$4,B$3+1,B$5/100,B$7,B$6,3,FALSE)/B$7*100


Book2
ABC
24769/30/2005 
247710/1/2005 
247810/2/2005 
247910/3/2005 
248010/4/2005 
248110/5/20050
248210/6/20050.012191781
248310/7/20050.024383562
248410/8/20050.036575342
248510/9/20050.048767123
248610/10/20050.060958904
248710/11/20050.073150685
248810/12/20050.085342466
248910/13/20050.097534247
249010/14/20050.109726027
249110/15/20050.121917808
249210/16/20050.134109589
249310/17/20050.14630137
249410/18/20050.158493151
249510/19/20050.170684932
249610/20/20050.182876712
249710/21/20050.195068493
249810/22/20050.207260274
249910/23/20050.219452055
250010/24/20050.231643836
250110/25/20050.243835616
250210/26/20050.256027397
250310/27/20050.268219178
250410/28/20050.280410959
250510/29/20050.29260274
250610/30/20050.304794521
250710/31/20050.316986301
250811/1/20050.329178082
250911/2/20050.341369863
251011/3/20050.353561644
251111/4/20050.365753425
251211/5/20050.377945205
251311/6/20050.390136986
251411/7/20050.402328767
251511/8/20050.414520548
251611/9/20050.426712329
251711/10/20050.43890411
251811/11/20050.45109589
251911/12/20050.463287671
252011/13/20050.475479452
252111/14/20050.487671233
252211/15/20050.499863014
252311/16/20050.512054795
252411/17/20050.524246575
252511/18/20050.536438356
252611/19/20050.548630137
252711/20/20050.560821918
252811/21/20050.573013699
252911/22/20050.585205479
253011/23/20050.59739726
253111/24/20050.609589041
253211/25/20050.621780822
253311/26/20050.633972603
253411/27/20050.646164384
253511/28/20050.658356164
253611/29/20050.670547945
253711/30/20050.682739726
253812/1/20050.694931507
253912/2/20050.707123288
254012/3/20050.719315068
254112/4/20050.7315068490.743699
254212/5/20050.743698630.743699
254312/6/20050.7558904110.75589
254412/7/20050.7680821920.768082
254512/8/20050.7802739730.780274
254612/9/20050.7924657530.792466
254712/10/20050.8046575340.829041
254812/11/20050.8168493150.829041
254912/12/20050.8290410960.829041
255012/13/20050.8412328770.841233
255112/14/20050.8534246580.853425
255212/15/200500
255312/16/20050.0121917810.012192
255412/17/20050.0243835620.048767
255512/18/20050.0365753420.048767
255612/19/20050.0487671230.048767
255712/20/20050.0609589040.060959
255812/21/20050.0731506850.073151
255912/22/20050.0853424660.085342
256012/23/20050.0975342470.097534
256112/24/20050.1097260270.13411
256212/25/20050.1219178080.13411
256312/26/20050.1341095890.13411
Sheet1
Cell Formulas
RangeFormula
B2476:B2563B2476=IF($A2476=$B$3,0,IF(AND($A2476>$B$3,$A2476<$B$4),B2475+$B$9,IF($A2476=$B$4,0,IF(AND($A2476>B$4,$A2476<=EDATE(B$4,B$8*12)),IF(AND(MOD(MONTH($A2476)-MONTH(B$4),12/B$6)=0,DAY(B$4)=DAY($A2476)),0,B2475+B$9),""))))
 

gcefaloni

Board Regular
Joined
Mar 15, 2016
Messages
117
There is a basis option in the ACCRINT function for using a 365-day year. Here is a revision with that option and a modified cumulative accrual formula that uses a series of IF statements to determine position on the calendar:
Book2
AB
1INT_ACC01285PBU1
2SECURITY_NAME
3ISSUE_DT10/5/2005
4FIRST_CPN_DT12/15/2005
5CPN4.45
6CPN_FREQ2
7PAR_AMT5000
8Maturity (y)20
9Daily Accrual0.012191781
Sheet1
Cell Formulas
RangeFormula
B9B9=ACCRINT(B$3,B$4,B$3+1,B$5/100,B$7,B$6,3,FALSE)/B$7*100


Book2
ABC
24769/30/2005 
247710/1/2005 
247810/2/2005 
247910/3/2005 
248010/4/2005 
248110/5/20050
248210/6/20050.012191781
248310/7/20050.024383562
248410/8/20050.036575342
248510/9/20050.048767123
248610/10/20050.060958904
248710/11/20050.073150685
248810/12/20050.085342466
248910/13/20050.097534247
249010/14/20050.109726027
249110/15/20050.121917808
249210/16/20050.134109589
249310/17/20050.14630137
249410/18/20050.158493151
249510/19/20050.170684932
249610/20/20050.182876712
249710/21/20050.195068493
249810/22/20050.207260274
249910/23/20050.219452055
250010/24/20050.231643836
250110/25/20050.243835616
250210/26/20050.256027397
250310/27/20050.268219178
250410/28/20050.280410959
250510/29/20050.29260274
250610/30/20050.304794521
250710/31/20050.316986301
250811/1/20050.329178082
250911/2/20050.341369863
251011/3/20050.353561644
251111/4/20050.365753425
251211/5/20050.377945205
251311/6/20050.390136986
251411/7/20050.402328767
251511/8/20050.414520548
251611/9/20050.426712329
251711/10/20050.43890411
251811/11/20050.45109589
251911/12/20050.463287671
252011/13/20050.475479452
252111/14/20050.487671233
252211/15/20050.499863014
252311/16/20050.512054795
252411/17/20050.524246575
252511/18/20050.536438356
252611/19/20050.548630137
252711/20/20050.560821918
252811/21/20050.573013699
252911/22/20050.585205479
253011/23/20050.59739726
253111/24/20050.609589041
253211/25/20050.621780822
253311/26/20050.633972603
253411/27/20050.646164384
253511/28/20050.658356164
253611/29/20050.670547945
253711/30/20050.682739726
253812/1/20050.694931507
253912/2/20050.707123288
254012/3/20050.719315068
254112/4/20050.7315068490.743699
254212/5/20050.743698630.743699
254312/6/20050.7558904110.75589
254412/7/20050.7680821920.768082
254512/8/20050.7802739730.780274
254612/9/20050.7924657530.792466
254712/10/20050.8046575340.829041
254812/11/20050.8168493150.829041
254912/12/20050.8290410960.829041
255012/13/20050.8412328770.841233
255112/14/20050.8534246580.853425
255212/15/200500
255312/16/20050.0121917810.012192
255412/17/20050.0243835620.048767
255512/18/20050.0365753420.048767
255612/19/20050.0487671230.048767
255712/20/20050.0609589040.060959
255812/21/20050.0731506850.073151
255912/22/20050.0853424660.085342
256012/23/20050.0975342470.097534
256112/24/20050.1097260270.13411
256212/25/20050.1219178080.13411
256312/26/20050.1341095890.13411
Sheet1
Cell Formulas
RangeFormula
B2476:B2563B2476=IF($A2476=$B$3,0,IF(AND($A2476>$B$3,$A2476<$B$4),B2475+$B$9,IF($A2476=$B$4,0,IF(AND($A2476>B$4,$A2476<=EDATE(B$4,B$8*12)),IF(AND(MOD(MONTH($A2476)-MONTH(B$4),12/B$6)=0,DAY(B$4)=DAY($A2476)),0,B2475+B$9),""))))

You, sir, are a freaking champ!

Thank you so much. This works perfectly! And with your explanations on top of it, I think I actually understand where I went wrong. Your help was extremely appreciated!
 

KRice

Well-known Member
Joined
Dec 9, 2003
Messages
1,061
Office Version
  1. 2019
Platform
  1. Windows
You're welcome...I'm glad to help. Have you given any more thought to the issue I mentioned about transitions from one period to another? In B9 we compute the normalized daily accrual amount. For this example, it is 0.01219; and every day moving forward, the cumulative interest should increase by this amount. We start at 0 on 10/5/2006. This suggests that if nothing is accumulated on 10/5/2005 but one day's worth of interest is added on 10/6/2005, then the interest is credited at the end of an accrual period. That is, the account is credited very late that same day and reported on the following day's account status report, or the credit is applied tomorrow for today's interest earnings. No issues so far.

But what happens on 12/14/2005, 12/15/2005, and 12/16/2005? The cumulative balance increases by one day on 12/14/2005, which we've established would be for earnings from either 12/13/2005 or for earnings of 12/14/2005 (and applied to the account late on 12/14)...I suspect they do the latter. So this normalized cumulative amount is paid out and the cumulative balance reset to 0....but the reset to 0 should occur on the payout date, and the following day should see an increase in cumulative balance by one day. Where is the increase in cumulative balance on 12/15/2005? This is why I believe an earnings day is missing, and this occurs every time there is a payout and the cumulative balance resets to 0. I believe the 12/15/2005 entry should not be 0, and instead it would be one of these two options:
1) It would reflect an increase in the normalized cumulative balance of 0.01219 that would be credited to the prior running balance 0.85342 (on 12/14) bringing the new cumulative balance to 0.8656, whereupon that amount (0.8656) is paid out on 12/15 while simultaneously reducing the cumulative balance to 0 (this would not be seen on the sheet). Then on the following day (12/16), the new cumulative balance would be 0.01219 to account for earnings on 12/16 (this is the amount we see for 12/16, but we don't see the earning for 12/15).
2) Payment is made on 12/14 or 12/15 for the cumulative amount shown on 12/14/2005....namely for 0.85342. Then on 12/15, the new cumulative amount shown would be 0.01219, followed by another daily increase on 12/16, bringing the new normalized cumulative amount to 0.02438 on 12/16.

Note that both of these options describe adding one more day's worth of interest earnings. The only difference being whether the interest is credited in time for the payout or whether it counts toward the cumulative balance in the next period. Do you have details that would resolve this issue? Otherwise, I still think that you're missing earnings around each payout transition.
 

gcefaloni

Board Regular
Joined
Mar 15, 2016
Messages
117
You're welcome...I'm glad to help. Have you given any more thought to the issue I mentioned about transitions from one period to another? In B9 we compute the normalized daily accrual amount. For this example, it is 0.01219; and every day moving forward, the cumulative interest should increase by this amount. We start at 0 on 10/5/2006. This suggests that if nothing is accumulated on 10/5/2005 but one day's worth of interest is added on 10/6/2005, then the interest is credited at the end of an accrual period. That is, the account is credited very late that same day and reported on the following day's account status report, or the credit is applied tomorrow for today's interest earnings. No issues so far.

But what happens on 12/14/2005, 12/15/2005, and 12/16/2005? The cumulative balance increases by one day on 12/14/2005, which we've established would be for earnings from either 12/13/2005 or for earnings of 12/14/2005 (and applied to the account late on 12/14)...I suspect they do the latter. So this normalized cumulative amount is paid out and the cumulative balance reset to 0....but the reset to 0 should occur on the payout date, and the following day should see an increase in cumulative balance by one day. Where is the increase in cumulative balance on 12/15/2005? This is why I believe an earnings day is missing, and this occurs every time there is a payout and the cumulative balance resets to 0. I believe the 12/15/2005 entry should not be 0, and instead it would be one of these two options:
1) It would reflect an increase in the normalized cumulative balance of 0.01219 that would be credited to the prior running balance 0.85342 (on 12/14) bringing the new cumulative balance to 0.8656, whereupon that amount (0.8656) is paid out on 12/15 while simultaneously reducing the cumulative balance to 0 (this would not be seen on the sheet). Then on the following day (12/16), the new cumulative balance would be 0.01219 to account for earnings on 12/16 (this is the amount we see for 12/16, but we don't see the earning for 12/15).
2) Payment is made on 12/14 or 12/15 for the cumulative amount shown on 12/14/2005....namely for 0.85342. Then on 12/15, the new cumulative amount shown would be 0.01219, followed by another daily increase on 12/16, bringing the new normalized cumulative amount to 0.02438 on 12/16.

Note that both of these options describe adding one more day's worth of interest earnings. The only difference being whether the interest is credited in time for the payout or whether it counts toward the cumulative balance in the next period. Do you have details that would resolve this issue? Otherwise, I still think that you're missing earnings around each payout transition.

The coupon payments do indeed accrue on the payment date but I will account for that in the total return calculation because I really want this sheet to reset to zero on the payment date. I double checked versus Bloomberg data and it seemed to line up perfectly after the latest changes you've suggested. I need to adapt the formula for floating rate bonds which tend to be a spread above US 3M T-Bills rather than a simple interest rate through time. Once I'm done with that. I will use price fluctuations and interest accrued daily to calculate total return as I had mentioned previously as being my ultimate goal. THank you so much once again.
 

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