Interest calculations - APR monthly conversion

cccrunch

Hi All,

Im struggling with interest conversions, I've read on the net that the way to work out your monthly or daily interest for your credit card is to take the APR, and then divide it by 12 or 365 respectively.

Well i've done this on an interest rate of 17.9APR

17.9/12 = 1.49167

However, if i look at MBNA's terms and conditions the say the following:

17.9% APR (variable) (1.3852% monthly)

Doing a search online i found the following converter that confirms MBNA's calculation: http://mathz.com/apr.php

So... is my calculation inccorect, and if so, what is the correct formula for establishing you monthly or daily interest rate from your APR?

Many thanks to the mathematicians out there!

Robert_Sterling_3

Yes your calculation is incorrect.
It is not that you got your sum wrong
It is that you did the wrong sum.

Let r be the Annual Rate of Interest

Let MR be the "So Called" Monthly Rate of Interest.

Then

MR = +100*[ [ 1 + ( +r/+100 )]^[+1/+12] -1]

This produces a result similar to the one you quoted from MBNA but not identical to it.

This is in part due to the fact that the 17.9% is expressed in only 3 significant figures.

The actual interest rate on the loan might be 17.949% for example.

Your incorrect Monthly Rate would give an Annual Rate 19.4%

cccrunch

Thanks Robert, I'm going to give it a try:money:

Robert_Sterling_3

The monthly interest is compounded 12 times each year.

cccrunch

Thanks Robert, i have the formula working now...

Based on the above, I have worked out the daily interest rate to be 0.04524%

How would i calculate the interest for the month (depending on how many days in the month there are)?

My Solution below based on a balance of £3000: anyone let me know if they think its incorrect?

Month Total = Principal(1+(dailyInterest/100))^nDays

?= 3000(1.0004524)^31
?= 3000(1,01411998709)
Month Total: £3042.356

Sorry, all this mathematical compounding stuff is enough to do my head in, but am trying to get a good understanding on how it works.

Robert_Sterling_3

I can show you how it would be done.
However when it is done on a real computer, not a micro computer, it might be done with a greater degree of accuracy.

For example when you calculate that the daily rate of interest is 0.04524%
even the microcomputer may go to a greater number of decimal place but then only exhibit accuracy to 4 significant figures.

At the end of each day the computer will "roll over"

Let the balance of the account at the end of day one be b1
To add the interest for day one we need to add b1*0.0004524
So the balance at the start of day two will be
b1 + b1*0.0004524 which is 1.0004524*b1
In mathematical rather than computer notation we would just omit the asterisk and write 1.0004524b1

Then at the end of day 2 you take that days final outstanding balance and again multiply it by 1.0004524

In a month of 28 days you would multiply by 1.0004524 28 times.

If there was no addition or subtraction of capital that month just the addition of interest

At the end of the month the final balance would be

(1.0004524^28)*b1 for 31 days (1.0004524^31)*b1



.....................................................................................................
For further mathematical advice check out my post headed "No Orchids for Miss Blandish" in the MSE Arms forum where I did a little experiment earlier this week. I posted two new threads one was No Orchids for Miss Blandish ,where I think there were three responses, and one called "What famous person do you think you might be mistaken for?" this one has has 1,600 viewing and 225 responses. Don't tell anyone else about this. This part of this message will be edited out in the very near future.

never-in-doubt

Robert_Sterling wrote: »

Yes your calculation is incorrect.
It is not that you got your sum wrong
It is that you did the wrong sum.

Let r be the Annual Rate of Interest

Let MR be the "So Called" Monthly Rate of Interest.

Then

MR = +100*[ [ 1 + ( +r/+100 )]^[+1/+12] -1]

This produces a result similar to the one you quoted from MBNA but not identical to it.

This is in part due to the fact that the 17.9% is expressed in only 3 significant figures.

The actual interest rate on the loan might be 17.949% for example.

Your incorrect Monthly Rate would give an Annual Rate 19.4%

My Lord! Now I am impressed.......... Carol Voderman eat your heart out :eek:

sloughflint

Robert_Sterling wrote: »

I can show you how it would be done.
However when it is done on a real computer, not a micro computer, it might be done with a greater degree of accuracy.

For example when you calculate that the daily rate of interest is 0.04524%
even the microcomputer may go to a greater number of decimal place but then only exhibit accuracy to 4 significant figures.

At the end of each day the computer will "roll over"

Let the balance of the account at the end of day one be b1
To add the interest for day one we need to add b1*0.04524
So the balance at the start of day two will be
b1 + b1*0.04524 which is 1.04524*b1
In mathematical rather than computer notation we would just omit the asterisk and write 1.04524b1

Then at the end of day 2 you take that days final outstanding balance and again multiply it by 1.04524

In a month of 28 days you would multiply by 1.04524 28 times.

If there was no addition or subtraction of capital that month just the addition of interest

At the end of the month the final balance would be

(1.04524^28)*b1 for 31 days (1.04524^31)*b1

Robert, you used 1.04524 rather than 1.0004524.

What you are saying in post 6 is merely confirming the process Op is stating in post 5 unless I'm missing something.

Not sure what level of accuracy is required but I made the daily rate:

[1.179^(1/365)]-1= 0.0004512 rather than 0.0004524

Robert_Sterling_3

never-in-doubt wrote: »

My Lord! Now I am impressed.......... Carol Voderman eat your heart out :eek:

Have a look at "No Orchids for Miss Blandish" in the Money Savers Arms Forum earlier this week.

This message will be edited out in the near future.

Robert_Sterling_3

sloughflint wrote: »

Robert, you used 1.04524 rather than 1.0004524.

What you are saying in post 6 is merely confirming the process Op is stating in post 5 unless I'm missing something.

Yes i forgot that it was a percentage

and yes he does appreciate what is going on.

Cheers.