debt

[jonah2.0]

Beer drenched approval follows.

Rate​

16%​

Initial Balance​

10,595​

​

Month​	Payment​	Interest​	Payment after Interest​	Ending Balance​
1​	250​	141.27​	108.73​	10486.27​
2​	250​	139.82​	110.18​	10376.09​
3​	250​	138.35​	111.65​	10264.44​

I thought to show my calculation for the first three months before I do it in the excel. What do you think of it?

It's all good.
I'll show you the so called Retrospective method of determining the outstanding balance at the end of the nth payment period in just a few minutes.

 

[jonah2.0]

Beer assisted reckoning follows.

Rate​

16%​

Initial Balance​

10,595​

​

Month​	Payment​	Interest​	Payment after Interest​	Ending Balance​
1​	250​	141.27​	108.73​	10486.27​
2​	250​	139.82​	110.18​	10376.09​
3​	250​	138.35​	111.65​	10264.44​

I thought to show my calculation for the first three months before I do it in the excel. What do you think of it?

If you implement the the odd-add rule of rounding in your excel spreadsheet, you'll find that the outstanding balance you get will correspond exactly with the theoretical balance of the Retrospective method. Well, almost, I think. I can't remember anymore. Alzheimer's is beginning to takeover my mind.

 

[logistic_guy]

Come on man

You're super Genius. Even if I read the chapter, I would not be able to come up with this shortcut formula.

SoooooooooO beautiful Sir jona$\displaystyle 2.0$

The idea is just to set up this formula and solve for $\displaystyle x$. I'll let $\displaystyle \text{W|A}$ do the calculations!

$\displaystyle 10595\left(1+\frac{0.16}{12}\right)^{x}-250\left[\left(1+\frac{0.16}{12}\right)^{x}-1\right]\frac{12}{0.16}=0$

$\displaystyle x \approx 63 \ \text{months}$

I will still do it with the excel and compare. I know that they should give the same result. Soon, I'll show you a screenshot!

 

[jonah2.0]

Beer assisted reckoning follows.

Come on man

You're super Genius. Even if I read the chapter, I would not be able to come up with this shortcut formula.

SoooooooooO beautiful Sir jona$\displaystyle 2.0$

The idea is just to set up this formula and solve for $\displaystyle x$. I'll let $\displaystyle \text{W|A}$ do the calculations!

$\displaystyle 10595\left(1+\frac{0.16}{12}\right)^{x}-250\left[\left(1+\frac{0.16}{12}\right)^{x}-1\right]\frac{12}{0.16}=0$

$\displaystyle x \approx 63 \ \text{months}$

I will still do it with the excel and compare. I know that they should give the same result. Soon, I'll show you a screenshot!

Thou art correct Mario.
That is just as beautiful.
62 months of 250 plus a smaller payment for the 63rd month.
I hope you've realized how much more detailed it is to work with Zima and Brown's books.
It's slightly easier with the amortization equation.

 

[jonah2.0]

Beer drenched ramblings follows.

Beer assisted reckoning follows.


Thou art correct Mario.
That is just as beautiful.
62 months of 250 plus a smaller payment for the 63rd month.
I hope you've realized how much more detailed it is to work with Zima and Brown's books.
It's slightly easier with the amortization equation.

View attachment 39185

It's strange that Maple gives a slightly different value from my Desmos reckoning.
Maybe it's because I used a fraction for the interest period.

 

[jonah2.0]

Beer drenched ramblings follows.

...
It's strange that Maple gives a slightly different value from my Desmos reckoning.
Maybe it's because I used a fraction for the ...

Freaking Maple calculator!

 

[jonah2.0]

Beer assisted reckoning follows.

...
I will still do it with the excel and compare. I know that they should give the same result. Soon, I'll show you a screenshot!

Using odd-add rule for rounding, we have

 

[jonah2.0]

How does your spreadsheet compare with mine?

 

[logistic_guy]

How does your spreadsheet compare with mine?

The negative sign in the $\displaystyle 63^{\text{rd}}$ month confirms that a partial payment will be paid in that month. So, yes we have the same sheets, except mine is not organized as yours. Also, I have not shown all the months!

What was wrong with $\displaystyle \text{Maple}$? Do you think that the absolute error for its logarithmic functions was only designed for $\displaystyle 5$ decimal places. For now, it's sufficient for finding the number of months, but for other calculations if the absolute error is much larger than, say $\displaystyle 10^{-13}$, I would not trust $\displaystyle \text{Maple}$.

 

[jonah2.0]

Beer induced ramblings follows.

... The negative sign in the $\displaystyle 63^{\text{rd}}$ month confirms that a partial payment will be paid in that month. So, yes we have the same sheets, except mine is not organized as yours. Also, I have not shown all the months!
...

You're e gonna have to do something about rounding them results to the nearest cent.
It's looks too messy. Otherwise, it's all good Mario.
You just need to reflect the final smaller payment.

 

[logistic_guy]

Beer induced ramblings follows.

You're e gonna have to do something about rounding them results to the nearest cent.
It's looks too messy. Otherwise, it's all good Mario.
You just need to reflect the final smaller payment.

But you did not round them to the nearest cent! Look the End Balance in the month $\displaystyle 62$, it is $\displaystyle 211.76613943$.

If it was rounded to the nearest cent, you would write $\displaystyle 211.77$, but your table shows $\displaystyle 211.76$!

 

[jonah2.0]

Beer induced ramblings follows.

But you did not round them to the nearest cent! Look the End Balance in the month $\displaystyle 62$, it is $\displaystyle 211.76613943$.

If it was rounded to the nearest cent, you would write $\displaystyle 211.77$, but your table shows $\displaystyle 211.76$!

The only rounding that's necessary is the one that takes place after multiplying the outstanding balance by 0.16/12. My spreadsheet automatically rounded the interest to two decimal places using the odd-add rule so that other automated spreadsheet calculations involved nothing more than addition and subtraction.

 

[logistic_guy]

Beer induced ramblings follows.


The only rounding that's necessary is the one that takes place after multiplying the outstanding balance by 0.16/12. My spreadsheet automatically rounded the interest to two decimal places using the odd-add rule so that other automated spreadsheet calculations involved nothing more than addition and subtraction.

View attachment 39206

But your rounding method will not give accurate results for the End Balance. For example, your End Balance for the month $\displaystyle 61$ is $\displaystyle 455.68$ when it actually must be $\displaystyle 455.69$.

 

[jonah2.0]

Beer induced wisdom follows.

But your rounding method will not give accurate results for the End Balance. For example, your End Balance for the month $\displaystyle 61$ is $\displaystyle 455.68$ when it actually must be $\displaystyle 455.69$.

Accurate in your view amounts to the theoretical outstanding balance without intermediate rounding.
Unfortunately, you're gonna have to compromise your views with actual practical financial practices where interest credits must be rounded to the nearest cent or whatever bank policy there is.

Edit: Let us continue this tomorrow. Getting too drunk. I seem to have detected an error in my spreadsheet.

 

[logistic_guy]

Beer induced wisdom follows.

Accurate in your view amounts to the theoretical outstanding balance without intermediate rounding.
Unfortunately, you're gonna have to compromise your views with actual practical financial practices where interest credits must be rounded to the nearest cent or whatever bank policy there is.

Edit: Let us continue this tomorrow. Getting too drunk. I seem to have detected an error in my spreadsheet.

According to the book's examples, it rounds the interest to $\displaystyle 2$ decimal places (which in turn rounds everything else to $\displaystyle 2$ decimal places), and then it let the sheet calculate the rest. Of course, it gives slightly different results than both of us, but at least it catches the number of months to pay the loan precisely.

 

[jonah2.0]

Brandy induced reckoning follows.

... I seem to have detected an error in my spreadsheet.

Yup, I made a pretty mess.
Managing Excel with just one's phone can be hazardous to one's health. Not very advisable; I would not recommend it at all. Commands and many features are hard to locate with a small screen.
Anyway, round 2.

 

[jonah2.0]

Comments to follow.

 

[logistic_guy]

This matches my recent calculations, except the last row! You did a great job to adjust it manually.



Adjusting last row manually