1. ## effective annual rate

Company B plans to give an incentive, a discount of 5% to its customers if they pay immediately, or credit terms of 50 days to settle the full amount. At what effective annual rate are these two payment options equivalent?

I am not very sure what the question is asking about. Is it asking the cost of forgoing the discount rate?

My work:

5/1, net 50

Period= 365/ (50-1) = 7.45

cost = 5%/ 95% = 0.053

Therefore the effective annual cost is 7.45 x 0.053 = 0.392 or 39.2%

Am i right? Thanks.

2. ## Re: effective annual rate

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

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

3. ## 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!!

4. ## Re: effective annual rate

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

5. ## Re: effective annual rate

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

6. ## Re: effective annual rate

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

100 / (1 + i)^50 = 95
i = .001026392...

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

7. ## Re: effective annual rate

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?

Yes.

9. ## Re: effective annual rate

Originally Posted by Wilmer
Yes.
Thanks, does simply multiplying the daily rate with 365 take into consideration the effects of compounding interest?

10. ## Re: effective annual rate

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.