Another one

[its_me]

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.

Answer r = 5.45%

[Svak]

Say the price is $100
i=0.12 annual effective

one-half month interest rate j = [(1.12)^1/24-1] = 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%

[its_me]

Sh*t

I took one-half month as ( 1.5 months)

[its_me]

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%.

Answer is 19.3655

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

[Svak]

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 = 1.10³=1.331
Effective discount rate for three years=0.2486

PV of the perpetuity = (Ia)_3^┐0.10 ÷ 0.2486 =19.365

[Gandalf]

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.