Can you help me to get the manual calc for get the result of the function PAGO from excel using the value of future value, for example this method
=PMT(0.0158,12,-300000,0.6*300000) return 13,900.50 if I remove the future value the function is =PMT(0.0158,12,-300000,0) and the result is 27,641.20
in this second example the function for get this value is ((Ir * (1 + Ir)^Np ) * M ) / ((1+ Ir)^Np -1)
where Ir = interes rate, Np number of payments and M the financing amount.
but Im not sure how I can add the additional value (future value) in this function.
The function is for calculating loan repayment installments. PV if Present amount of the loan outstanding. FV is the loan amount that will be outstanding after the NPER(number of installments) payments.
So, can there be different amounts outstanding FVs for the same loan at the same time?
If you are planning to calculate loan installments in blocks of periods. Say 12 months, 18 months and hence, there will be different FVs at different times. But in that case you should have a new cell for calculation. Where FV of previous block will become PV for calculation block.
More the PV more will be the result amount
More the FV less will be the result amount
Please see if image below helps.
Link
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'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
School Question:
Build a function retirement_age(PMT, i, FV, start_age) that calculates the (whole) age at which your customer can retire, if they:
Invest an amount, PMT at the END of every YEAR (with the first
payment made exactly one year from now),
at an interest rate of i% per year, compounded annually.
They require an amount of AT LEAST FV in order to be able to afford
retirement.
They just turned start_age years old.
I am struggling to solve the number of years PMT would take to reach FV
This is my code:
def retirement_age(PMT, i, FV, start_age):
count = 0
while PMT <= FV: #PMT set to loop till it reaches FV
PMT = PMT * (1+i)
count = count + 1 #adds 1 to count value until while loop satisfied
age = count + start_age #adds count value to start_age to determine retirement age
return int(age) #returns age
print (retirement_age(20000, 0.1, 635339.63, 20))
my answer with this code:
57
The answer is supposed to be:
35
I can't tell what I'm doing wrong. And the task specifically mentions that we are not allowed to import external functions like math for example, which means I can't use math.log() which would probably solve all my problems.
First, I'll note that broad debugging questions like this aren't very appropriate for SO.
Having said that, I played around with it and after reading the specs again, I found the issue(s). I figured I might as well post it.
You only need to keep calculating while the principal is less than the future value. You can stop once they're equal.
The main issues however were that you aren't adding any money each year. You're just accumulating interest on the initial principal. And...
You invested PMT immediately. The investment doesn't happen until the end of the year, as the instructions emphasize. That means at the start of the looping, he has 0 invested. That means he doesn't start accumulating interest until the start of the second loop/year.
def retirement_age(PMT, i, FV, start_age):
age = start_age
p = 0
while p < FV:
p = PMT + p * (1+i)
age += 1
return int(age)
print(retirement_age(20000, 0.1, 635339.63, 20))
# 35
I introduced p to keep track of the running balance since it's separate from what's being added each year. Your logic for keeping track of age was also a little convoluted, so I simplified it down a bit.
I am trying to create a forecast tool that shows a smooth growth rate over a determined number of steps while adding up to a determined value. We have variables tied to certain sales values and want to illustrate different growth patterns. I am looking for a formula that would help us to determine the values of each individual step.
as an example: say we wanted to illustrate 100 units sold, starting with sales of 19 units, over 4 months with an even growth rate we would need to have individual month sales of 19, 23, 27 and 31. We can find these values with a lot of trial and error, but I am hoping that there is a formula that I could use to automatically calculate the values.
We will have a starting value (current or last month sales), a total amount of sales that we want to illustrate, and a period of time that we want to evaluate -- so all I am missing is a way to determine the change needed between individual values.
This basically is a problem in sequences and series. If the starting sales number is a, the difference in sales numbers between consecutive months is d, and the number of months is n, then the total sales is
S = n/2 * [2*a + (n-1) * d]
In your example, a=19, n=4, and S=100, with d unknown. That equation is easy to solve for d, and we get
d = 2 * (S - a * n) / (n * (n - 1))
There are other ways to write that, of course. If you substitute your example values into that expression, you get d=4, so the sales values increase by 4 each month.
For excel you can use this formula:
=IF(D1<>"",(D1-1)*($B$1-$B$2*$B$3)/SUMPRODUCT(ROW($A$1:INDEX(A:A,$B$3-1)))+$B$2,"")
I would recommend using Excel.
This is simply a Y=mX+b equation.
Assuming you want a steady growth rate over a time with x periods you can use this formula to determine the slope of your line (growth rate - designated as 'm'). As long as you have your two data points (starting sales value & ending sales value) you can find 'm' using
m = (y2-y1) / (x2-x1)
That will calculate the slope. Y2 represents your final sales goal. Y1 represents your current sales level. X2 is your number of periods in the period of performance (so how many months are you giving to achieve the goal). X1 = 0 since it represents today which is time period 0.
Once you solve for 'm' this will plug into the formula y=mX+b. Your 'b' in this scenario will always be equal to your current sales level (this represents the y intercept).
Then all you have to do to calculate the new 'Y' which represents the sales level at any period by plugging in any X value you choose. So if you are in the first month, then x=1. If you are in the second month X=2. The 'm' & 'b' stay the same.
See the Excel template below which serves as a rudimentary model. The yellow boxes can be filled in by the user and the white boxes should be left as formulas.
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)).