I'm always paying, never make it, but you can't look back

[venta]

So, sums. I can, broadly speaking, do sums. I have a degree in maths.

However, interest rate calculations have always baffled me. Sure, if you ask me to calculate 3 months compound interest at a monthly rate of x% I know what to do. However, when it comes to real examples of mortgages and credit cards, I can't work out what the sum I need to do is. I'm still slightly baffled about the interest charged me when I was a day late paying my credit card off in full in March.

Today, the BBC carried a story about a loanshark. It includes the following statement about someone who borrowed £1000:

"...to pay £49 a week over 60 weeks, making the total amount he had to
repay £2,940 at 917% APR."

Now, if we approximate 60 weeks to a year, then surely that's an annual interest rate of no more than 294%. The quoted APR isn't even in vaguely the right ballpark.

So... have I completely failed to understand APR ? (Wikipedia's page on the subject didn't really help with the definition.) Or is the BBC publishing unmitigated wank in the name of investigative journalism ?

Edit It turns out I'd failed to understand APR, and the BBC is cleared in this instance.

Comments

[chrisvenus]

Yeah, I'm struggling with that too... you can simplify by setting i and f to 0 which knocks out a few terms and makes the while loop:


do {
fx=a*(Math.pow(x,n+1)-x)/(x-1)-p;
dx=a*(n*Math.pow(x,n+1)-(n+1)*Math.pow(x,n)+1)/Math.pow(x-1,2);
z=fx/dx; x=x-z;
//alert("fx="+fx+"\ndx="+dx+"\nz="+z+"\nx="+x)
}
while (Math.abs(z)>1e-9);
r=100*(Math.pow(1/x,m)-1);


And then the last line of that basically implies to me that x = 1/weekly interest rate.

I think they are then using some kind of iterative process of approximations to find a value of x whcih satisfies the equations. It stops when z is very close to 0 which means that fx must be much much smaller than dx.

I suspect dx is worked out in some clever way. It looks vaguely like a differential and I suspect if I'd done more computer programming I'd recognise some technique of using differentials to get closer to an approximation of something...

The initial value fx basically has two terms the p on the end and the other bit. The first bit is basically decaying your repayments to simulate interest. You should note that Math.pow(x,n+1)-x)/(x-1) is a power series that can be expanded to x^n+x^(n-1)+...+x^2+x. When multiplied by a this is your repayments decaying by the interest rate. Personally I find it easier to see when you divide through by x^n and set interest = 1/x since you will then see the more intuitive series of each repayment having interest applied to it and them adding up to the total loan amount with interest added.

I've worked out now also that my discrepancy came purely from taking the first repayment off before applying interest. If I always apply interest before repayment then I get the same 917% that the BBC quote (I should also mention that in my inintial comment above I forgot to take the 100% off for the initial loan amount).