## The Math Behind Excel’s CUMIPMT() & CUMPRINC() Functions

I published the math behind the CUMIPMT() & CUMPRINC() functions at the bottom of my spreadsheet for the post Annuity – Excel Functions and Math. I think it got lost in all the annuity math. When I Google the math for these two functions, my blog doesn’t show up until the 6th or 7th page, depending on the wording of the search. I see the question asked without a real answer, so I am posting the formulas again by themselves. I am also doing it because it is my blog and I can.

Download “CUM Also the math for a single row of a simple amortization schedule: Download “CUM Don Pistulka

Retired Credit Union CFO - Finance
Background: over 40 years in investments, asset/Liability management, banking, securities trader.
Worked for: California Credit Union, WesCorp, CalFed S&L, Crocker Bank, Carroll McEntee, Federal Home Loan Bank Board (D.C.), Western Asset Management, Security Pacific National Bank.

### 19 Comments

1. Aigerim

Hello!

How did you get payment \$2302?

I’ve got 41666 by this calc 100000*5/(12*(1-pow((1+(5/12)),-48)))

2. Aigerim

hello!

how did you get payment \$2302?

is there anything wrong in my calculations 100000*5/(12*(1-pow((1+(5/12)),-48)))?
I get 41667 everytime

1. =PMT(0.05/12,48,100000)=2,302.93

=100000*0.05/(12*(1-(1+(0.05/12))^-48))=2,302.93

3. José Luis

There is any way to use CumIPmt in a matrix range?
Ex: {SUM(CumIPmt (i/q;n;p;b;e;0)}

1. Don Pistulka

Hi Jose,
I’m not sure what you are asking for. Could you send me an Excel workbook with an example of what you would like the matrix to look like?
blog@pistulka.com

Don

4. Bell Boy Wonder

Dear Don

Based on your excel file, CUMPRINC requires i,q,n,p,b,e for parameters. But your function requires i,q,m,p,b,e. How to convert “n” parameter in CUMPRINC to “m” parameter in cell G14/G17

1. Don Pistulka

Converting the Excel inputs to m only needs p, i, and n.
m=p*i/(12*(1-(1+(i/12))^-n))

Don

1. Atul

If we have rate of interest calculated on monthly basis, does this become
m = balance * apr / (1 – 1 / ((1 + (apr)) ** term))

1. Don Pistulka

Atul,

Almost,
m=balance*apr/12/(1-1/(1+apr/12)^term)

Using the default data on my example:
2,302.93=p*i/12/(1-1/(1+i/12)^n)

Unless you meant that the rate was divided by 12, before calculating the formula. Then your formula would work.

Don

2. Aigerim

Hello!

How did you get payment \$2302?

this 100000*5/(12*(1-pow((1+(5/12)),-48))) gives me 41666.66895195165 not 2302

5. Keldon

Hi

The CUMIMPT formula does not make use of the payment amount (m), however, your mathematical formula does use it. As much as you are getting the same result as the formula, I would imagine there is a different mathematical formula powering the function.

1. Don Pistulka

Hi Keldon,
The reason the Excel formula does not ask for M (payment) is that the inputs it does ask for are enough to calculate the payment. So asking for the payment is not necessary.
Don

6. Badz

amazing!!!! Thank YOU!!!!

1. Don Pistulka

Thanks You

7. […] The Math Behind Excel’s CUMIPMT() & CUMPRINC() Functions July 22, 2015 […]

8. dsfsdsdfsfd

Exactly what I was looking for. Thanks!

1. Don Pistulka

Glad I could help