Starting payment when increase rate is known & total payment is kn

[Guest]

Does anyone know of a function that can provide the the starting payment and
the subsequent payments thereafter to reach a total as defined.

Example:
Total payments must be 5000 over 5 years. The increase rate is 10% every
year, so what will the starting payment be.

I have been able to figure this out using Algebra type mathematical
formula's in excel, however i believe there must be a function that can very
easily achieve this more quickly. The field Total payments, no of payments
and increase rate is known, while the unknown is the starting payment and the
payments subsequent to that.

 

[Guest]

assuming you want a ten percent increase each year based on that years payment
to get the first payment
=5000/sumproduct(1.1^(row(A1:A5)-1)))
to get the second payment
=1.1* this cell
and so forth

 

[Fred Smith]

You have a simple future value problem. Your future value is 5000, interest rate
10% and term 5 years. Use:

=pmt(10%,5,0,-5000,0)

 

[Guest]

Dear BJ,

Thank you for the prompt response, however your suggestion returns first
payment 147.30 when the result should be 818.99. I think we on the right
track here, but somehow the function is not 100% correct. Also it seems you
have used some Algebra type formuals here which are a lot more simpler than
what i have used. Can you please explain your logic so that i can understand
this.

 

[Dana DeLouis]

have used some Algebra type formuals here which are a lot more simpler

than
what i have used.

If you are looking for the Formula:

=(10%*5000)/((10%+1)^5-1)

->818.89

 

[Guest]

other than I added one too many ")" at the end of the formula in the response
when I typed it
I am not sure why you get 147.30
I get 818.98 with the equation as printed minus the ")"
I can get 147.30 with
=5000/SUMPRODUCT(1.1^(ROW(A19:A23)-1))

the function is the same as 5000/(1.1+1.1^2+1.1^3+1.1^4+1.1^5)
since row(A1)=1 row(A2) =2 etc
so 1.1^(row(A1)-1)=1.1^(1-1)=1.1^(0)=1.1
and sumproduct was a convenient function to use for summing)

 

[Guest]

Dear BJ,

I have figured out that the formula you suggested must always start in row
1, since row A1 = 1 and using the formula in any other row will result in
incorrect calcuation.

Thank You for your assistance in this

 

[Guest]

Dear Dana,

Thank you for this, this is a simpler formula to what i have used.

 

[Guest]

Dear Fred,

Thank you for this, I looked at this formula and tried this before but could
not figure this out, as the unknown was the present value. But I have learnt
something from this as the present value in your formula is "0". Can you
explain the logic here, i am assuming this is because this value is unknown
and can be replaced with "0".
--
Thank you in advance

You have a simple future value problem. Your future value is 5000, interest rate
10% and term 5 years. Use:

=pmt(10%,5,0,-5000,0)

 

[Dana DeLouis]

...the formula you suggested must always start in row 1...

...and using the formula in any other row will result in incorrect
calcuation.

Just some thoughts...
To avoid such an issue as you described, that technique is usually written
like this.

=5000/SUMPRODUCT(1.1^(ROW(INDIRECT("1:5"))-1))

... 1.1+1.1^2+1.1^3+1.1^4+1.1^5

However, such series have a closed form. Sounds like this was the issue you
were facing.
Do a Google search for " Geometric Series"
What you were looking for was something like this:
total = start * (Geometric Series)

Than, solve for start value.

You will recognize the Geometric Series formula in Excel's help under the PV
function.

 

[joeu2004]

I have figured out that the formula you suggested must always start in row
1, since row A1 = 1 and using the formula in any other row will result in
incorrect calcuation.

Notwithstanding the fact that the formula is overkill, you might have
run into a problem if you copy-and-pasted the formula. The relative
range A1:A5 should be written as an absolute range, namely:

=5000/sumproduct(1.1^(row($A$1:$A$5)-1))

In this context, row($1:$5) always works.

 

[joeu2004]

Notwithstanding the fact that the formula is overkill,[....]

"Overkill" was a poor choice of words. I think BJ's solution is the
most natural, given the problem description. It is just that it can
be simplified, as others have demonstrated.

 

[Fred Smith]

It's because there is no present value. You are starting from zero. It's
actually very common in PMT formulas.

--
Regards,
Fred

Dear Fred,

Thank you for this, I looked at this formula and tried this before but could
not figure this out, as the unknown was the present value. But I have learnt
something from this as the present value in your formula is "0". Can you
explain the logic here, i am assuming this is because this value is unknown
and can be replaced with "0".