A plea for help to the numerically literate

Dziekanowski

I'm in the throes of trying to buy a car and, while I have enough in savings to be able to buy the car outright, I am trying to calculate whether or not I would be better off to use the dealer's credit and tuck my money away in the meanwhile.

Here's the scenario:

I have told the dealer that if he can benefit me to the tune of £317.50 then we have a deal.

I currently have £12,000 in a Nationwide e-Savings account. This account, in theory, pays 5.8% AER. I have told the dealer that if he can offer a favourable enough credit agreement (he's indicated that he has room for manoeuvre on his interest rates), then my savings will remain in this account and will drip-feed his loan each month (via my current account on a standing order) until the balance is cleared.

So, the first thing I need to do is calculate what the £12,000 would be worth in 5 years (the length of the proposed credit agreement) time if it were left where it is. My crude understanding of calculating interest rates tells me that the calculation I should do is the following:

12,000 * (1+0.058/365)^(5*365)

This works out at £16036.76

Herein lies my first problem.

Using my (possibly flawed) formula, £10,000 locked away in this account for one year should be worth £10,597.10.

However, according to Nationwide's calculator at this link http://www.nationwide.co.uk/nbsasp/illustrator/default.asp, it will only be worth £10,588.80. I can't for the life of me work out how they've come up with this figure but until I can figure out how to calculate the interest properly then I can't really go much further.

Assuming that Nationwide have got it wrong (which they obviously haven't but pretending they have allows me to finish explaining what I am trying to do) my car dealer needs to put together a credit agreement with repayments totalling £15,719.26 over 5 years.

This brings me onto my next issue. I think that he is calculating the interest on the loan in a different way. His verbal illustration was based on £12,000 at 4.5% over 5 years. In order to calculate the monthly repayments on this, he did the following calculation:

((12,000 / 100) * (100 + 4.5 * 5)) / 60

which equates to a monthly repayment of £245 and a total balance payable of £14,700.

What I can't work out here is whether or not this way of calculating interest is working against me or not - and this is where my head really starts spinning. Something in my head is telling me that there should be some kind of reverse coupound, sliding scale mathematics going on here as I eat into the capital and that by calculating it the way he has I am paying more interest than I should - but I can't, for the life of me, work out precisely how this should work!

On a final note, I am aware that I need to deduct tax from my savings and factor that in but, once I am confident I know how to do the maths, I'll recalculate and factor that in afterwards.

Oh, and I also realise that it doesn't make sense to leave the money in that Nationwide account for the full term but this is what I have told the dealer I am going to do and I don't intend letting on that I intend investing it more prudently while it is in my hands (I was thinking of using AngloIrish Bank's 1, 2, 3 and 4 year fixed rate bonds instead to try to work the arrangement further in my favour).

Any help on deciphering the calculations that I need to be performing will be gratefully received!

jonesMUFCforever

IMO it is never sensible to borrow your own money.
You will almost certainly pay more for the loan than you would get in credit interest.
eg his verbal quotation at 4.5% - is this a flat rate or APR. I would think it is a flat rate so the true APR will be around 9%.
You also quote 5.8% from your e-savings account - I take it that this is before tax so the net rate is 4.02%.

As I see it you are going to lose out by taking out the finance.

CLAPTON

several things

-you may be better using your skills to get him to reduce the price a bit more (have you tried phoning other dealers and getting their best price for cash ).

-your calculation of interest is incorrect. although interest is earned on a daily basis, it is only capitalised on a monthly or yearly basis.
so 'compounding' is monthly or yearly and not daily as your formula assumes.

as far as the dealers figures are concerned only deal with a written quote etc that you can take away and study at your leisure. obviousy dont even think about PPI.

they often quote 'flat rates' obviously to confuse...should be called fraud.

its very very very unlikely that it will work out at less than 5.8% (less net of tax?)

Dziekanowski

Quick update.

Part of my riddle has been solved in that Nationwide have 'fessed up and admitted that their calculator is, erm, mis-calculating.

I dare say that were I of the inclination to push it far enough they may be forced to honour some kind of compensation or increased rate as a gesture of goodwill for misadvertising but the bottom line is that the rate is a plain and simple 5.80% AER and not 5.888% AER as the calculator suggests.

Cheers for the help anyway, folks.

jonesMUFCforever

It does not make much difference to your calculation though.

nomoneytoday

The dealer is using a rate of 4.5% FLAT !

This is just under 9% APR as it doesn't take into account your payments in the mean time.

In year 1 the £12000 loan costs £540 in interest. As it does in year 5, even though you would have been paying the loan off..

Even allowing for the Nationwide rounding error, you would be better off paying the loan off without dealer finance..