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#1
04-05-2004, 11:02 PM
 its_me Member Join Date: Jan 2003 Location: AO Posts: 1,774
Another one

A store permits its customers to pay with credit card or to receive a % discount (r) for paying cash .For credit card purchases, the business gets 95% of purchase price one-half month later. At an eff annual rate of 12%, the 2 options are equivalent. Find r.

#2
04-05-2004, 11:25 PM
 Svak Member Join Date: Jun 2002 Location: Lost Posts: 150

Say the price is \$100
i=0.12 annual effective

one-half month interest rate j = [(1.12)<sup>1/24</sup>-1] = 0.004733

Customer can pay
100(1-r) now OR
95 one-half month later using credit card.

PV of 95 = (95/1.004733)

Equate both and solve for r = 1- [(95/1.004733) (1/100)]

=5.447%
__________________

#3
04-06-2004, 10:13 AM
 its_me Member Join Date: Jan 2003 Location: AO Posts: 1,774

Sh*t

I took one-half month as ( 1.5 months)
#4
04-09-2004, 07:57 PM
 its_me Member Join Date: Jan 2003 Location: AO Posts: 1,774

What is the PV of a perpetuity -immediatewith pmts of 1,2,3,1,2,3,1,2,3.... assuming annual eff r.o.i 10%.

i am getting 10 . My Equation is

i got a-angle-3/(1-v^3) at i = .10 as my final expression,

cud also be
la- angle-3 (at i=.10 ) * 1/(id) ( at i = (1.1)^3 - 1 )

and i have no idea where i am going wrong
#5
04-09-2004, 08:49 PM
 Svak Member Join Date: Jun 2002 Location: Lost Posts: 150

One way to do:

Think of this in terms of a 3 year increasing annuity immediate.

PV of this increasing annuity immediate is received at beginning of every third year forever.

Effective interest rate for three years = 1.10<sup>3</sup>=1.331
Effective discount rate for three years=0.2486

PV of the perpetuity = (Ia)<sub>3<sup>┐</sup>0.10</sub> ÷ 0.2486 =19.365
__________________

#6
04-09-2004, 10:53 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,563

The same math as Svak, with a slightly different order of operations.

Think of it as three perpetuities-immediate, each making payments once every three years. The present value of such a perpetuity, 3 years before the first payment, is 1/0.331.

We have the perpetuity paying 3 in years 3,6,9,...; its value at 0 is 3/0.331

We have the perpetuity paying 2 in years 2,5,8,...; its value at -1 is 2/0.331; at 0 is 2.2/0.331.

We have the perpetuity paying 1 in years 1,4,7,...; its value at -2 is 1/0.331; at 0 is 1.21/0.331.

Total is 6.41/0.331.

I think Svak's way of looking at it is better (more likely to be useful when you face a slightly different problem in the future), but it's good to remember there are lots of ways to attack TOI questions. If you don't remember the "right" way, don't give up.

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