Re: effective annual rate

Find the interest rate at which 0.95 now is equivalent to £1 in 50 days,

$\displaystyle 0.95(1+i)^{\frac{50}{365.25}} = 1$

i get about 45%

Re: effective annual rate

This kind of "effective rate guessing" is usually kept simple (it was in my days anyway!):

50 days = .05

365 days = .05 / 50 * 365 = 36.5 %

One thing is definite:

there is no way anything precise can be determined,

since we're not told what rate the company borrows at;

if it can borrow at something lesser than what the 5%/50days represents,

you can be sure it won't offer that discount!!

Re: effective annual rate

Thanks again Wilmer, how is your method different from SpringFan's method?

Re: effective annual rate

I disagree, as long as "equivalent" means "has same NPV" the borrowing rate is not relevent.

Re: effective annual rate

(95).....................................[50days]100

100 / (1 + i)^50 = 95

i = .001026392...

365i = .374633... ; so ~37.5 % = "effective annual rate"

Re: effective annual rate

Quote:

Originally Posted by

**Wilmer** (95).....................................[50days]100

100 / (1 + i)^50 = 95

i = .001026392...

365i = .374633... ; so ~37.5 % = "effective annual rate"

what does the interest rate i=.001026392 represent? The daily interest rate for the year?

Re: effective annual rate

Re: effective annual rate

Quote:

Originally Posted by

**Wilmer** Yes.

Thanks, does simply multiplying the daily rate with 365 take into consideration the effects of compounding interest?

Re: effective annual rate

Quote:

Originally Posted by

**hooke** Thanks, does simply multiplying the daily rate with 365 take into consideration the effects of compounding interest?

No. The resulting .374633 (or ~37.5%) is the annual rate compounded daily

(same as a car loan quoted as 12% compounded monthly; results in 12.6825% effective).

The actual effective annual rate is .454552, or ~45.5% : as per Spring Fan's post.

My point earlier was that the "lender" will declare 12% annual cpd. monthly,

not 12.6825%...looks cheaper to the borrower!

But I should have kept my trap shut and "stick to the facts"! (as SpringFan did).

This is what it all looks like:

Code:

`DAY INTEREST BALANCE`

000 950.0000

001 .9751 950.9751

002 .9760 951.9511

...

049 1.0243 998.9747

050 1.0253 1000.0000 : BINGO!

051 1.2639 1001.2639

...

364 1.4150 1380.0530

365 1.4165 1381.4695

365.25 .3543 1381.8238 **

** 1381.8238 / 950 = 1.454552, hence ~45.46% effective.