How to calculate interest

squishy_2

I've got an opportunity to have 4.6% on my debt for 6 months - how will the interest on this be calculated as I understand it's an annual percentage rate?

Thanks...

MMCG_2

This is how I always calculate my interest for the following month. Take the 4.6%APR. Divide it by 12, to give your monthly interest rate, 0.383. Now take the amount you owe for example - £5000 and multiply it by the monthly figure. Now divide it by 100 to get the interest amount in £ and p. for the first month. £19.17 interest.

For the next month, subtract what your last payment was then repeat the above. I don't have a formula for calculating the payment over the year in one go though. Just a bit of time and a sharp pencil. Maybe someone else out there has a faster method. I hope this helps though as it gives you an idea of waht interest to add each month to your debt before the statement arrives.

YorkshireBoy

squishy wrote: »

I've got an opportunity to have 4.6% on my debt for 6 months - how will the interest on this be calculated as I understand it's an annual percentage rate?

Use this calculator http://www.stoozing.com/mon2yr.htm to work out the 'annual non-compounded equivalent rate'...sometimes shown as the 'simple annual rate' (SAR) on provider summary boxes.

Your interest per month, assuming a static balance, is then...

Balance x SAR(%) / 365 x n

where n = number of days in the statement period.

Using MMCG's assumed balance...

£5,000 x 4.51% / 365 x 31 days (for March) = £22.64

NickX

YorkshireBoy wrote: »

Your interest per month, assuming a static balance, is then...

Balance x SAR(%) / 365 x n

YorkshireBoy, do they definitely work the interest to the number of days in the month ?

The only card I have paid interest on is Barclaycard, and they seemed to just divide the % by 12, then multiply by the balance.

From actuarial point of view, dividing by 12 or 365 is not correct, the percentage should have a power of (1/12) or (1/365) applied to correctly calculate compound interest.

squishy_2

Thank you so much, this helps a lot!!!

YorkshireBoy

First of all, let me say that I based my post on my understanding of how it works. I have no insider knowledge.

NickX wrote: »

YorkshireBoy, do they definitely work the interest to the number of days in the month ?

I didn't say "month" Nick. I was very careful to say the "number of days in the statement period", which will be 28/29/30/31 depending on the month in question.

Interest is actually calculated, and accrued, daily on the daily posted balance. That's why, to make things easier to calculate, I assumed a static balance. If the balance is changing daily, then the interest charged to the account will be the sum of 28/29/30/31 individual figures.

From actuarial point of view, dividing by 12 or 365 is not correct, the percentage should have a power of (1/12) or (1/365) applied to correctly calculate compound interest.

I'm not sure I agree. Interest accrues daily (on the closing posted balance) but only compounds (and therefore forms part of the next statement period's opening balance) monthly...unless I've misunderstood your post?

NickX

OK thanks, I have no insider knowledge either.

But my understanding is that an APR is an Annual Percentage Rate, basically an annualized rate which can be used for comparison purposes.

If the Daily Rate is x, then the calculation to work out the APR is as follows :

(1 + x/100) ^ 365

To work out the Daily Rate from the APR the calculation is reversed, so if the APR is y, then the Daily rate is :

(1 + y/100) ^ (1/365)

This is the basis of Compound interest. I would then expect the interest to accrue on a daily basis.

However, this is the theory, in practice I think they do as you have said and divide the annual rate by 365 to get the daily rate.

It is actually quite complicated and I'm sure the banks computer systems will be carefully programmed to apply the correct calculations.

NickX

Ah, OK OK just read your post again.

My ramblings refer to APR (Annual Percentage Rate)

Your calculations refer to SAR (Simple Annual Rate)

I understand now, the calculation with powers is for APRs, the calculation with division is for SARs.

YorkshireBoy

As I say, it's only my understanding (and I failed my maths GCSE ...but thankfully I got the hang of it later ) but the same principle applies to savings accounts when interest is paid monthly.

Many people use the AER when in fact they should use the gross p.a. rate / 365 to calculate the daily interest.

So, to compare credit cards with savings accounts, my understanding is that...

APR is the equivalent of AER, and

SAR is the equivalent of gross p.a.

YorkshireBoy

thepelican wrote: »

From what I understand, the AER does not always equal the APR.

For clarity, I've edited my post to say "is the equivalent of" rather than "=".

AER considers the compounding effect of interest, whereas APR may not. In some instances, the APR more closely resembles the 'SAR'

But I may be wrong...

You are.

The AER or Annual Equivalent Rate is the official rate for savings accounts, and is designed to allow easy comparisons as it's meant to smooth out the variances between accounts (it's the equivalent of the APR for debts).

http://www.moneysavingexpert.com/banking/interest-rates#AER

See also the text accompanying the calculator which I linked to in post #3.