# effective annual rate

• Aug 10th 2012, 09:46 PM
hooke
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.
• Aug 11th 2012, 05:38 AM
SpringFan25
Re: effective annual rate
Find the interest rate at which 0.95 now is equivalent to £1 in 50 days,

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

• Aug 11th 2012, 06:52 AM
Wilmer
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!!
• Aug 11th 2012, 10:18 AM
hooke
Re: effective annual rate
Thanks again Wilmer, how is your method different from SpringFan's method?
• Aug 11th 2012, 12:47 PM
SpringFan25
Re: effective annual rate
I disagree, as long as "equivalent" means "has same NPV" the borrowing rate is not relevent.
• Aug 11th 2012, 06:15 PM
Wilmer
Re: effective annual rate
(95).....................................[50days]100

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

365i = .374633... ; so ~37.5 % = "effective annual rate"
• Aug 11th 2012, 10:48 PM
hooke
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?
• Aug 11th 2012, 11:06 PM
Wilmer
Re: effective annual rate
Yes.
• Aug 11th 2012, 11:13 PM
hooke
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?
• Aug 12th 2012, 06:21 AM
Wilmer
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.