Interest Rate Calculation (one for economists)

Michael Collins

I was trying to figure out the differnt terminology related to taking out loans. I came across this Wiki entry on the various terms:

Ok so what the article says is that a 10% APR loan is equivalent to:

1) 0.7974% effective monthly interest rate
2) 9.569% annual interest rate compounded monthly
3) 9.091% annual rate in advance.

So the first 2 are grand I see where they come from:

1): 0.7974% each month would give an APR of (1+0.007974)^12 - 1 = 10%

2): 9.569% compounded monthly means a twelfth of that percent added to the accumulating principle value each month or an APR of (1+0.09569/12)^12 -1 = 10%

3): Ok so the real problem here, I guess, is I don't know what it means specifically by annually in advance? The way it gives a value with 3 decimal points suggests that you can work it out somehow.

Any finance people out there able to work this one out?

RefulgentGnomon

Don't know what the term means but I can guess where the figure is coming from. It is 1/11 so maybe 0.1/1.1?

Michael Collins

Ah. Didn't notice that. That helps somewhat alright, I might be able to figure it out from here. Thanks

Colonel Sanders

seems to be the equivalent rate of discount (d) to use.

(1-d) = 1/(1+i) (=v)

d = i/(1+i)

MathsManiac

Do you think the rationale behind the nomenclature could go like this:

"I'm going to lend you EUR110 for a year. I'm charging you 9.091% for that priviledge, which I'm going to take in advance. That's 10 for me, which you're giving me back immediately, and here's your 100, which you're going to give me back at the end of the year."

Weird, I know, but its the only way I can make half-sense of it.

Yakuza

Discounted rates aren't used for loans, they're for purchasing future debts.

The rationale here is "Someone is going to give you €110 in a year's time, I'll give you €100 now for it and claim the €110 in a year's time".

That way, you're getting €10 less than the amount, but you're getting it now. The discount is €10/€110, or 9.09%

There! I knew umpteen years of Actuarial exams would come in (vaguely) useful some time!

Another way of viewing it is that €100 is the present value (v) of €110 in one year's time, at 10% interest.

babytooth

yeah its like ecp (commerical paper).

you pay in advance.

assuming simple interest.

100 euro in 1 year.
you borrow the amount 100/1.1 = 90.91....
its been badly laid out in the wilki ref.

RedJoker

It's the compound monthly discount rate. d = i / (1+i)

It's used for annuities paid in advance.

Present value:

An = (1 + v^n) / d

where v = 1 / (1+i)

Accumulated (future) Value:

Sn = ((1+i)^n) - 1 / d

The wiki reference is fine once you understand what in advance means. It means that all payments get shifted back one time unit, so your first payment happens at t = 0 instead of t = 1. For example, you pay your sky subscription in advance.