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ventaSo, 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.
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.
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no subject
Date: 2008-08-04 09:33 am (UTC)My working is as follows. There is a recurrence relation relating the amount you owe this week after a repayment to the amount you owed last week:
cn+1 = cn(1+i) – r
Eliminating the recursion gives this:
cn = c0(1+i)n – r(1+i)n-1 – … – r(1+i) – r
where the right-hand side is a geometric series which can be simplified thusly:
cn = c0(1+i)n – r((1+i)n–1)/i .
So the repayment r in terms of the initial amount of credit c and interest rate (per week) i is:
r = cik/(k–1) where k = (1+i)n .
Now presumably they've done their recurrence relation the other way about and ended up with
c = rx(xn–1)/(x–1) where x = 1/(1+i)
but the two formulae are equivalent, it turns out.