Interest rate maths...

Kev64

Trying to juggle all my cards around - yet again - (and getting sick of doing it to be honest !), and I've got my spreadsheet with all the cards and balances on, plus each company's current balance transfer deals (if any). I'm trying to work out which is cheaper, but I'm having trouble with the maths !

e.g. Lloyds are offering 4.9% apr for six months with a 3% fee. How does this compare to leaving a balance on my Virgin card at 15.9% apr ?
Which is cheaper for the six months ?

Does it work out like this... 4.9% + 3% = 7.9% for 6 months ? (thereby saving me 15.9-7.9= 8% of interest for six months ?)... and at the end of those six months, I would have to transfer it elsewhere (as Lloyds are extortionate on their regular rates), so should I factor in the fee I would get charged then too ? - or doesn't that count ?

I'm rather confused about it all !

Many thanks in advance for any assistance !

hax_2

If you want to work out the interest rate from 6 months to 12 months you have to square the number instead of doubling it. Likewise you square root an annual interest rate to get a 6 month one. So your 15.9% APR would be

(1.159^0.5) - 1 = 7.657% for 6 months

EDIT: Yes, your 3% fee does count as well.

Kev64

When you say it counts, do you mean the inital 3% fee gets added to the 6 month rate i.e. 4.9% + 3% = an effective rate of 7.9% ?

I'm just trying to calculate what the effective interest rates would be for a) leaving it where it is (i.e. 7.657% for six months) versus transferring it to Lloyds (what I'm trying to calculate !). I'm trying to get both figures on a level playing field so to speak, so I can work out the effective interest rate (including allowing for charges) for moving to Lloyds, so I can immediately see if it's worth it or not.

I'm also trying to work out if I need to factor in the fee (whatever that is) when I need to transfer the money again at the end of the 6 months, as in theory (my theory anyway !), if I leave the money where it is, I'll be charged 15.9% apr with no extra charges (or 7.657% from your calculation for the 6 months). If I transfer the balance to Lloyds, I'll be charged 4.9% for 6 months, but I'll have to pay a 3% fee to move it there, then very likely another fee to transfer it elsewhere when the Lloyds deal comes to an end in 6 months time. Should I consider that fee in my calculations now, or is that only to be considered in the maths for the eventual transfer away from Lloyds in 6 months time (i.e. is it only relative to whatever deal I'm transferring to at that point). ?

If any of that makes sense !

opinions4u

The fee is key.

1) It's paid up front, not spread over the period you are borrowing for.
2) It then accrues interest on itself (with some issuers at a higher rate than the introductory offer).

If the charges for a 3% fee were spread across a calendar year, the APR for the fee alone would be 3%. Because it's payable up front, that nearly doubles an APR to 5.9% (ish).

Because you are condensing that in to a 6 month period (instead of a year) the true cost of the fee would probably be quoted at somewhere above 10% if it had to be quoted as an APR. Then add on the 4.9% as well.

Up front balance transfer fees on short term deals are rarely good value and should be avoided if possible.

Stinkybell

It makes more sense if you do this with actual numbers... lets go for £1000, and you paying off £150 a month (yes, the amount you pay off is important!)

Staying with Virgin at 15.9% APR --> 1.325% per month
Month 1: £1000 - £150 = £850 x 1.325% = £861.26
Month 2: £861.26 - £150 = £711.26 x 1.325% = £720.69
Month 3: £720.69 - £150 = £570.69 x 1.325% = £578.25
Month 4: £578.25 - £150 = £428.25 x 1.325% = £433.92
Month 5: £433.92 - £150 = £283.92 x 1.325% = £287.68
Month 6 £287.68 - £150 = £137.68 x 1.325% = £139.51

Going to Lloyds at 4.9% APR --> 0.408% per month, plus 3% fee
Month 1: £1000 - £150 = £850 x 0.408% = £853.47 + £30 fee = £883.47
Month 2: £883.47 - £150 = £733.47 x 0.408% = £736.46
Month 3: £736.36 - £150 = £586.46 x 0.408% = £588.85
Month 4: £588.85 - £150 = £438.85 x 0.408% = £440.64
Month 5: £440.64 - £150 = £290.64 x 0.408% = £291.83
Month 6 £291.83 - £150 = £141.83 x 0.408% = £142.41

So in my example you are better staying where you are, as the fee makes up for thedrop in interest. Also double check how Lloyds apply interest to BT fees, as I have just made an assumption here

hax_2

Ok...we need to convert the Lloyds 4.9% APR to 6 months. Normally we would need to do this:

1.049^0.5 - 1

However because there is a 3% fee, you would pay interest on this fee also. So the correct calculation would be:

[(1 + 5.047%)^0.5] - 1= 2.492% for 6 months
because 4.9 x 1.03 = 5.047 (I hope I haven't confused you at this point!)

You would then add 3% to the 2.492% to give you 5.492%, which is less than 7.657% 6 months interest for Virgin.

Like you said correctly, when the Lloyds promotional offer ends you'll need to make another balance transfer and incur another balance transfer fee. On the other hand if you left the balance on your Virgin card and found a better offer than Virgin then you'll have to pay a balance transfer fee anyway. Unfortunately its difficult to decide whether to include this fee in your calculations now, because it depends what offers are available in the future and whether you're likely to be approved for the credit cards that have those promotional offers.

What's the standard APR for the Lloyds CC when the promotional offer ends? Is it the same as Virgin (15.9%)?

hax_2

opinions4u wrote: »

The fee is key.

1) It's paid up front, not spread over the period you are borrowing for.
2) It then accrues interest on itself (with some issuers at a higher rate than the introductory offer).

I stand corrected - Lloyds do charge a higher interest rate for the fee. Some lenders don't, but Lloyds do:

http://forums.moneysavingexpert.com/showpost.html?p=27270921&postcount=5

I would need to know the Lloyds standard APR.

cos_2

I think Tom Lehrer said it better:

Consider the following subtraction problem, which I will put up here: 342 -
173.

Now remember how we used to do that. three from two is nine; carry the one, and
if you're under 35 or went to a private school you say seven from three is six,
but if you're over 35 and went to a public school you say eight from four is
six; carry the one so we have 169, but in the new approach, as you know, the
important thing is to understand what you're doing rather than to get the right
answer. Here's how they do it now.

You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens,
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add them to the two and get twelve,
And you take away three, that's nine.
Is that clear?

Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place.

From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right.)
And so you have thirteen tens,
And you take away seven,
And that leaves five...

Well, six actually.
But the idea is the important thing.

Now go back to the hundreds place,
And you're left with two.
And you take away one from two,
And that leaves...?

Everybody get one?
Not bad for the first day!

Hooray for new math,
New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!
Now that actually is not the answer that I had in mind, because the book that I
got this problem out of wants you to do it in base eight. But don't panic. Base
eight is just like base ten really - if you're missing two fingers. Shall we
have a go at it? Hang on.

You can't take three from two,
Two is less than three,
So you look at the four in the eights place.
Now that's really four eights,
So you make it three eights,
Regroup, and you change an eight to eight ones,
And you add them to the two,
and you get one-two base eight,
Which is ten base ten,
And you take away three, that's seven. Ok?

Now instead of four in the eights place
You've got three,
'Cause you added one,
That is to say, eight, to the two,
But you can't take seven from three,
So you look at the sixty-fours.

"Sixty-four? How did sixty-four get into it?" I hear you cry.
Well, sixty-four is eight squared, don't you see?
(Well, you ask a silly question, and you get a silly answer.)

From the three you then use one
To make eight ones,
And you add those ones to the three,
And you get one-three base eight,
Or, in other words,
In base ten you have eleven,
And you take away seven,
And seven from eleven is four.
Now go back to the sixty-fours,
And you're left with two,
And you take away one from two,
And that leaves...?

Now, let's not always see the same hands.
One, that's right!
Whoever got one can stay after the show and clean the erasers.

Hooray for new math,
New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Come back tomorrow night. We're gonna do fractions.

Hope that helped? :rotfl:

Kev64

hax wrote: »

I stand corrected - Lloyds do charge a higher interest rate for the fee. Some lenders don't, but Lloyds do:

http://forums.moneysavingexpert.com/showpost.html?p=27270921&postcount=5

I would need to know the Lloyds standard APR.

At this moment, it's on a 0% deal until mid January, but after that it reverts to.... wait for it.... 26.52% APR :eek:

I was on the phone to them last night querying this, as I have an excellent credit score (now !) and have been a Lloyds customer for over 30 years, and they're advertising the card I have as a '11.9% Typical'. They are looking into it...

Anyway, I don't know what (if) the interest rate on the fee would be..

Moggles_2

Kev64 wrote: »

I don't know what/if the interest rate on the fee would be.

LloydsTSB treats BT fees as purchase transactions, so you would incur some interest. Other things being equal, this would be charged at your standard rate for purchases, whatever that happens to be (please refer to your monthly statements).