I would like to know the following: in the FV formula, can I use both the PMT and PV or I should use either the PMT or the PV?
The problem is the following:
You have invested 75000 in a trust fund at r=0,075. You will draw $12000 per year from this fund for 4 years, starting at the end of the year 7.
What will be the amount that will be left over in this fund at the end of the year 10?
The correct calculation is to find the FV of $75000 at the end of year 10 and then to subtract the accumulated PMT over the last 4 years.
However, I calculated the FV(period=7) and then by using FV(period=7) as a PV, I tried to calculate the FV(at period=10) by using both PMT and PV [which equals FV(period=7)]. At the end I get the wrong number. What it's wrong with it?
What happens if I use both PMT and PV in the FV formula? I assumed that based on the PV [which equals FV(period=7)], the formula subtracted each time the corresponding PMT and thus at the end (period=10) the remaining value would be the "left over" in period 10. But I don't get the correct number. So what happens if I use both the PV and PMT in the FV formula? What is the number I get by using both PMT and PV?
Any help would be appreciated! Thanks a lot!
What happens if I use both PMT and PV in the FV formula?
Essentially the same as if you used them individually (ceteris paribus) and then added their results.
This is not entirely intuitive (IMO) as the timing of the future value is different. I suspect that is your issue with trying to recalculate part way through the term, but it is impossible to be sure without your actual numbers.
A simple example, assuming annual or a one off payment of 100 at 10% pa for three years:
Three formulae shown emboldened and their results on the same line. Running through the steps in English:
Receive 100 at the start of Year1 so are liable for 10 interest at the end of that year (110 outstanding).
Receive 100 at the start of Year2 so are liable for interest on (110+100) at the end of that year =21 (231 outstanding).
Receive 100 at the start of Year3 so are liable at the start of Year3 for 331.00.
Receive 100 at the start of Year1 so are liable for 10 interest at the end of that year (110 outstanding).
At the end of Year2 further interest, of 11, outstanding.
At the end of Year3 further interest, of 12.1, outstanding, total then 133.10.
Moral: Seems to be, don't use both in the same formula :)
Related
Known that:
FV function: future value of constant payments at constant interest rate
FVschedule function: future value of no payments at variable compound interest
My task is to calculate the future value of constant payments at variable interest rate.
Say the principal is 10,000. Annual rate is 5%. Tenor with 2 monthly period starting at Jan. The periodic payment in arrear is 1,300.
Interest for Jan is calculated as (10,000 * 5% * 31 / 360 = 43) The principal repaid is (1,300 - 43) = 1,257.
Interest for Feb is calculated as ((10,000-1,257) * 5% * 28 / 360 = 34) The principal repaid is (1,300 - 34) = 1,266.
The future value (aka balloon payment) would be 10,000 - 1,257 - 1,266 = 7,477.
So I would like to know if there is a formula could calculate 7,477 by inputting the above data, rather than calculate the whole repayment schedule each time.
Thank you for your help.
I do not think there is such a function. There is however a way how to approach this in an excel-like manner. As you correctly anticipated, excel is just the right tool for that, as it can re-calculate the whole repayment schedule each time, many times a second.
First, collect the parameters like that to the columns K & L
Second, create a table with the schedule. First column label Date and it will be the date of the last days of the months. Lets assume that you start with the first day of the current month, so the first row will be
=EOMONTH($L$6;[#Period])
where $L$6 is the cell with start date. The next column [#Period] has just the count of the schedule periods, i.e. 1,2,3,4... as many as you like. You can use formula
=ROW()-1
for that.
Next column label Days with formula
=DAY([#Date])
That is for calculating the effective interest rate.
Next column label Aliquote with formula
=[#Days]/$L$2
with the effective interest rate for the current period (month).
Now it gets interesting. The next columns label B/O for the beggining of month outstanding amount
=$L$4-SUM(G$1:G1)
and copy/past for the next rows. It calculates the outstanding amount based on the principal parameter stored in L4 by subtracting the sum of Amortizations in the column G we create next.
Next column is then labeled interest
=$L$3*[#Aliquote]*[#[B/O]]
where L3 refers the parameter with the nominal interest rate.
and the next column is labeled Amortization
=$L$5-[#Interest]
calculated from the periodic arrears stored in L5.
The last column is labeled C/O for the close of the month outstanding amount.
=[#[B/O]]-[#Amortization]
If you have done it correctly, it shows you the C/O values running towards zero and then of course negative in the 8th period onward. You can change the parameters to get adjust it for the scenario you need.
I have an excel sheet with about 50,000 records where I need to find the number of minutes between two date timestamps but I need to exclude any minutes that occurred during the times we are not working.
Our schedule is M-F 8:30am-5:30pm, Saturdays 8:30am-1:30pm
We don't work Sundays or holidays.
As an example
Cell B2: [7/3/2020 2:16:21 PM]
Cell C2: [7/6/2020 9:20:23 AM]
The manually calculated answer for this one should be about 244 minutes. Task started Friday afternoon, Saturday was a holiday, don't work Sundays, task completed at 9:20am on Monday.
Usually, I come here and start writing a question and by the time I've understood my own problem well enough to post a question I have figured it out on my own but not this time! Help!
Update:
#ForwardEd shared this...
=((I2-H2)
-MAX(0,(NETWORKDAYS.INTL(H2,I2,"0000011",$M$2:$M$12)-1+(WEEKDAY(I2,1)=7)))*TIME(15,0,0)
-MAX(0,(NETWORKDAYS.INTL(H2,I2,"1111101",$M$2:$M$12)-(WEEKDAY(I2,1)=7)))*TIME(19,0,0)
-NETWORKDAYS.INTL(H2,I2,"1111110",$M$2:$M$12)-(NETWORKDAYS.INTL(H2,I2,"0000000")
-NETWORKDAYS.INTL(H2,I2,"0000000",$M$2:$M$12)))*24*60
Where H:H is the Start Date Timestamp and I:I is the Response Date Timestamp and M2:M12 contains my holiday list.
It worked beautifully until I ran into an example like this:
H2 - 07/26/2020 7:48:45 PM
I2 - 07/27/2020 8:57:58 AM
The net result was -650.78333. It looks like anything that starts one one day and ends on the next is coming back as negative.
We want to measure the average response time in minutes for the applications that require manual underwriting. These start timestamps are times that loan applications were received online so they could come in any time of day. The stop times are timestamps that represent the system recorded response time. i.e. the timestamp where an underwriter first did something with the loan application. If a loan application was received at 7pm and was not auto-decisioned then a manual underwriter will need to do something with it the next day when we start working.
If that application came in at 7pm on Wed and is decisioned by an underwriter at 8:46am on Tuursday, we would want to document 16 minutes for that application - not 826 counting the hours between 7pm and 8:30am.
What you want to look at is NETWORKDAYS.INTL. Use this in conjunction with the custom settings to determine the number of Saturdays, Sundays and for the number of days in between your start and end time. You know you have X amount of time per day that is non working time, and Y amount per Saturday.
Then you formula in essence becomes
(End time - start time) - X * No. Weekdays - Y * No. Saturdays - No. Sundays - No. Holidays
Now there will be some tricks in there in order to count your days. but that is the gist of what it boils down to in a formula.
The formulas that are doing the brunt of the work are:
WORKDAY
NETWORKDAYS.INTL
TIME
I avoided the use of an if statement by using a boolean operation that excel will resolve from TRUE/FALSE to 1/0 when sent through a math operator. Side note: I read somewhere that this is also faster than an IF statement, but have no way of proving it and really does not matter on a small number of calculations.
WORKDAY
This formula will return the day of the week for a given date, and a set day of the week to be 1. It will be need in this solution to determine if the end date is a Saturday which has a value of 7 in default setup up as well when option 1 is picked. The format for the formula is:
WORKDAY(Excel Serial date, day 1 of the week)
For this solution
WEEKDAY(B3,1)
NETWORKDAYS.INTL
This formula will be used to count the number of specific days a start and an end date. It can exclude a custom weekend or count a custom week. If it is supplied with a list of dates that are holidays they can be excluded as well. The basic format of the formula is:
NETWORKDAYS.INTL(Start Date, End Date, Custom week choice or workweek pattern, range of holiday dates)
When entering the formula it will give you a list of predefined options for the weekend choices. It will not talk about the pattern.
The pattern is a string 7 digits long consisting of 1 or 0. 0's represents the days you want to count and 1's are days you want to ignore. An important part of the pattern is that the first entry is MONDAY. "1010111" would count only Tuesdays and Thursdays.
TIME
Excel stores date as an integer. 1 represents 1st of January 1900, 2 the 2nd of January 1900 and so on. Time is stored as a decimal or if you prefer the percentage/fraction of a day or 24 hour period. So rather than figuring out the math to determine what percentage of a day X number of hours is, it is simpler to let excel calculate it for us and make the number a little more understandable to someone who may be deciphering the formula later. The basic format of the formula is:
TIME(Hours, Minutes, Seconds)
So as stated earlier, 6 key components need to be determined:
X - Amount of non working time after a weekday
Y - Amount of non working time after a Saturday
Number of weekdays
Number of Saturdays
Number of Sundays
Number of holidays
1) Determine Weekday Non-Working Hours
Based on the supplied information that work day stops at 1730 and starts as 0830. There are a couple of ways of doing the math. Subtract the working hours from 24 hours or count the non work hours at the end of the day and add them to the non work hours at the start of the day.
24 - (17.5 - 8.5) = 15
or
(24 - 17.5) + (8.5 - 0) = 15
For this example 15 will be hard coded into the final formula
2) Determine Saturday Non-Working Hours
Similar to above. Note that we are ignoring Sunday as it is a designated non working day which we already know is 24 hours or 1 day. We are just interested in the time between end of shift Saturday and start of the next normal working Monday. So it really gets calculated the same with just with difference end of shift time.
24 - (13.5 - 8.5) = 19
or
(24- 13.5) - (8.5 - 0) = 19
For this example 19 will be hard coded into the final formula
3) Determine Number of Weekdays
Based on the description earlier of of NETWORKDAYS.INT and working with the assumption that holidays are stored in the range F2:F2, and using a pattern of "0000011" the number of weekdays the formula will be as follows:
=NETWORKDAYS.INTL(B2,B3,"0000011",F2)
For this example the formula is place in cell F6
4) Determine Number of Saturdays
Similar 3) adjust the pattern to only select Saturdays by using "1111101"
=NETWORKDAYS.INTL(B2,B3,"1111101",F2)
For this example the formula is place in cell F7
5) Determine Number of Sundays
Similar 4) adjust the pattern to only select Saturdays by using "1111110"
=NETWORKDAYS.INTL(B2,B3,"1111110",F2)
For this example the formula is place in cell F8
6) Determine Number of Holidays
To get the number of holidays there is not a direct way of doing it. Instead take the difference between all days counted without holidays being factored in and all days counted with holidays counted in.
=NETWORKDAYS.INTL(B2,B3,"0000000")-NETWORKDAYS.INTL(B2,B3,"0000000",$F$2:F2)
For this example the formula is place in cell F9
Now at this point I would love to say just substitute all of the above into the generic formula, but there are a couple of special cases that need to be taken care of. You may have also noted I have not used the WEEKDAY formula yet.
So in order to count the number of days to which X is going to apply, its really the number of days minus 1. The minus 1 is because you want to cont the intervals between days, not the number of days themselves. This gets a little bit more trickier when the end day is a Saturday because there is still an interval there but Saturday is not counted as a weekday. So the True count for number of weekday intervals is:
=MAX(0,(F6-1+(WEEKDAY(B3,1)=7)))
I originally had the MAX(0, calc) in there to prevent the posibility of the day count being negative. After arriving at this final format it may not be needed and you might get away with the following but its untested:
=F6-1+(WEEKDAY(B3,1)=7)
This same concept needs to be applied to your Saturday count. If you job ends on Saturday you do not need to subtract the non working hours after the last Saturday. You formula will look like:
=MAX(0,(F7-(WEEKDAY(B3,1)=7)))
and again further testing is required to make sure MAX can be removed, but if it can then the formula would look like:
=F7-(WEEKDAY(B3,1)=7)
So now with the understanding how dates and times are stored, determine the time difference between start end end time and subtract all the non working hours.
=(B3-B2)-MAX(0,(F6-1+(WEEKDAY(B3,1)=7)))*TIME(15,0,0)-MAX(0,(F7-(WEEKDAY(B3,1)=7)))*TIME(19,0,0)-F8-F9
Now you will not want to use helper cells, so you can take each of the individual formula from F6 to F9 and wind up with:
=(B3-B2)-MAX(0,(NETWORKDAYS.INTL(B2,B3,"0000011",F2)-1+(WEEKDAY(B3,1)=7)))*TIME(15,0,0)-MAX(0,(NETWORKDAYS.INTL(B2,B3,"1111101",F2)-(WEEKDAY(B3,1)=7)))*TIME(19,0,0)-NETWORKDAYS.INTL(B2,B3,"1111110",F2)-(NETWORKDAYS.INTL(B2,B3,"0000000")-NETWORKDAYS.INTL(B2,B3,"0000000",$F$2:F2))
The formula looks unruly, but is easier to understand when broken down into its parts.
Now the last step is to get the answer to display in minutes. There are two choices.
You can leave it as it is in an excel serial date format and change the formatting of to a custom format of [m]. The [ ] will force it into minutes and prevent spill over to hours. It will also round to the nearest minute.
You can convert the results to minutes by multiplying by 24*60 and the value will be in minutes and decimal of minutes.
Note that:
A11 has Time formatting applied
A12 has General formatting applied
A14 has custom formatting of [m] applied
It should be something like this:
Create a calendar table with the workinghours for each days in the year you have data in
Date | StartTime | End time
1/1/2020 1/1/2020 8:30:00 PM 1/1/2020 5:30:00 PM
...
7/3/2020 7/3/2020 8:30:00 PM 7/6/2020 5:30:00 PM
...
12/31/2020
Then paste this code in a module
Function CalcDays(dStart As Date, dEnd As Date, daysCalendar As Range)
Dim Cell As Range
Dim MinDaysCalendar As Date, MaxDaysCalendar As Date
Dim aWSF As WorksheetFunction
Set aWSF = Application.WorksheetFunction
'check the minimum en the maximum date in the calendar
With aWSF
MinDaysCalendar = .Min(daysCalendar)
MaxDaysCalendar = .Max(daysCalendar)
End With
'if the date you check is not in the calendar, exit the function
If dStart < MinDaysCalendar Or dStart > MaxDaysCalendar Then
MsgBox "Date not in calendar"
Exit Function
End If
If dEnd < MinDaysCalendar Or dEnd > MaxDaysCalendar Then
MsgBox "date not in calendar"
Exit Function
End If
'sum the time of all the dates between the start and the end
'pick min and max in order to start and stop at the right time per day
Dim tempTime As Integer
With daysCalendar
For i = 1 To .Rows.Count
If .Cells(i, 2).Value >= CLng(dStart) And .Cells(i, 3).Value <= CLng(dEnd) Then
daytime = aWSF.Max(.Cells(i, 2).Value, dStart) - aWSF.Min(.Cells(i, 3).Value, dEnd)
End If
tempTime = tempTime + daytime
Next i
End With
'return the total time
CalcDays = tempTime
End Function
You can call the function by typing =calcdays in a cell and then give the startDay, endDay and calendar column as parameters.
There might still be some flaws in this code but I think we can manage those.
I'm trying to calculate the remaining balance of a home loan at any point in time for multiple home loans.
Its looks like it is not possible to find the home loan balance w/ out creating one of those long tables (example). Finding the future balance for multiple home loans would require setting up a table for ea. home (in this case, 25).
With a table, when you want to look at the balance after a certain amount of payments have been made for the home loan, you would just visually scan the table for that period...
But is there any single formula which shows the remaining loan balance by just changing the "time" variable? (# of years/mths in the future)...
An example of the information I'm trying to find is "what would be the remaining balance on a home loan with the following criteria after 10 years":
original loan amt: $100K
term: 30-yr
rate: 5%
mthly pmts: $536.82
pmts per yr: 12
I'd hate to have to create 25 different amortization schedules - a lot of copy-paste-dragging...
Thanks in advance!
You're looking for =FV(), or "future value).
The function needs 5 inputs, as follows:
=FV(rate, nper, pmt, pv, type)
Where:
rate = interest rate for the period of interest. In this case, you are making payments and compounding interest monthly, so your interest rate would be 0.05/12 = 0.00417
nper = the number of periods elapsed. This is your 'time' variable, in this case, number of months elapsed.
pmt = the payment in each period. in your case $536.82.
pv = the 'present value', in this case the principle of the loan at the start, or -100,000. Note that for a debt example, you can use a negative value here.
type = Whether payments are made at the beginning (1) or end (0) of the period.
In your example, to calculate the principle after 10 years, you could use:
=FV(0.05/12,10*12,536.82,-100000,0)
Which produces:
=81,342.32
For a loan this size, you would have $81,342.32 left to pay off after 10 years.
I don't like to post answer when there already exist a brilliant answer, but I want to give some views. Understanding why the formula works and why you should use FV as P.J correctly states!
They use PV in the example and you can always double-check Present Value (PV) vs Future Value (FV), why?
Because they are linked to each other.
FV is the compounded value of PV.
PV is the discounted value at interest rate of FV.
Which can be illustrated in this graph, source link:
In the example below, where I replicated the way the example calculate PV (Column E the example from excel-easy, Loan Amortization Schedule) and in Column F we use Excel's build in function PV. You want to know the other way... therefore FV Column J.
Since they are linked they need to give the same Cash Flows over time (bit more tricky if the period/interest rate is not constant over time)!!
And they indeed do:
Payment number is the number of periods you want to look at (10 year * 12 payments per year = 120, yellow cells).
PV function is composed by:
rate: discount rate per period
nper: total amount of periods left. (total periods - current period), (12*30-120)
pmt: the fixed amount paid every month
FV: is the value of the loan in the future at end after 360 periods (after 30 year * 12 payments per year). A future value of a loan at the end is always 0.
Type: when payments occur in the year, usually calculated at the end.
PV: 0.05/12, (12*30)-120, 536.82 ,0 , 0 = 81 342.06
=
FV: 0.05/12, 120, 536.82 , 100 000.00 , 0 = -81 342.06
I am trying to solve an iterative problem in Excel. I want to be able to calculate the sum of rent for x years. The rent is increasing at a rate of 10 percent every year. I quickly came up with this python code on a REPL for clarity:
year = 6
rent = 192000
total_rent = rent
for x in range(1 , year):
rent= rent + .1*rent
total_rent = total_rent + rent
print(total_rent) # 1481397.12 is what it prints
This is a trivial problem in programming but I am not sure the best way to achieve this in excel.
In excel I am doing it this something like this:
But all the intermediate rent amount(s) are not really needed. I guess there should be a for loop here as well too, but is there a mathematical representation of this problem which I can use to create the expected result?
If you have a financial problem, you might try the financial functions of excel.
=-FV(0.1, 6, 192000)
or
=FV(0.1, 6, -192000)
the detail: FV on Office Support
Description
FV, one of the financial functions, calculates the future value of an investment based on a constant interest rate. You can use FV with either periodic, constant payments, or a single lump sum payment.
Syntax
FV(rate, nper, pmt, [pv], [type])
For a more complete description of the arguments in FV and for more information on annuity functions, see PV.
The FV function syntax has the following arguments:
Rate Required
The interest rate per period.
Nper Required
The total number of payment periods in an annuity.
Pmt Required
The payment made each period; it cannot change over the life of the annuity. Typically, pmt contains principal and interest but no other fees or taxes. If pmt is omitted, you must include the pv argument.
Pv Optional
The present value, or the lump-sum amount that a series of future payments is worth right now. If pv is omitted, it is assumed to be 0 (zero), and you must include the pmt argument.
Type Optional
The number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0.
Your problem is a geometric series where the initial term is a = 192000 and the common ratio is r = 1.1. (The ratio is not just the 10% added, it includes the 100% that is added to.) To refresh your Algebra II memory, a geometric series is
total = a + a*r + a*r**2 + ... + a*r**(n-1)
The closed-form formula for the sum of the geometric series is
total = a * (r**n - 1) / (r - 1)
(using Python syntax), or, using something closer to Excel syntax,
total = a * (r^n - 1) / (r - 1)
where n is the number of years. Just substitute your values for a, r, and n.
As the question is about excel it is possible by
Or by using the FV function.
FV returns the future value of an investment based on regular payments and a constant interest rate.
Attributes of the FV function;:
Rate: The interest rate per period.
Nper: The total number of payment periods in an annuity.
Pmt: The payment made each period; it cannot change over the life of the annuity. Typically, pmt contains principal and interest but no other fees or taxes. If pmt is omitted, you must include the pv argument.
Pv: The present value, or the lump-sum amount that a series of future payments is worth right now. If pv is omitted, it is assumed to be 0 (zero), and you must include the pmt argument.
Type: The number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0.
Yet another way is computing it as a geometric series with the non-financial function SERIESSUM:
=SERIESSUM(1.1,0,1,192000*{1,1,1,1,1,1})
The rate multiplier is 1.1, starting from 1.1^0 == 1 and increasing by 1 each year. The result is 1*a + 1.1*b + 1.1^2*c.... The array 192000*{1,1,...} provides the coefficients a, b, c, ... : one array value for the initial total_rent = rent, and one for each subsequent year 1..5 (from range(1,year)).
I have quite the tricky pickle; I have a piece of sales data which has Grand Value, Monthly Fee and Contract Term.
It looks like this.
Grand Value Monthly Fee Contract Term (months)
$100.00 $20.00 5
$120.00 $10.00 12
$120.00 $10.00 24
The first thing you might notice that the last entry value looks wrong; it isn't, it is the annual value of that sale, not the total value. It is calculated elsewhere as "est revenue" but that's irrelevant to the question.
What I need to do is get an accurate view on the current years value, not the total value over x number of years.
In layman terms, the query i'd like to write is "give me the product of multiplying the Monthly_Fee by Contract_Term by 12, but if less than 12 multiply by Contract_Term instead".
Currently the best query I have is
=SUM(Data!Monthly_Fee:Monthly_Fee)*12
Which just lazily multiplies the monthly fee by 12.
Any excel masters care to help?
If I understand you correctly, this should work:
=SUMPRODUCT(Data!B2:B4,--(Data!C2:C4<12),Data!C2:C4)+SUMPRODUCT(Data!B2:B4,--(Data!C2:C4>=12)*12)
(obviously change the cell references)