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Please help me TVM question. Confusing [P/Y] = 1 with [P/Y]= different number

Find the present value of $3000 due in 5 years and 6 months if money is worth 4.5% compounded quarterly.

P1: I tried:

P/Y = 1

N = 5.5 x 4= 22

FV = 3000

I/Y = 4.5 / 4 = 1.125

CPT PV ==> -2345

=====

P2: I tried:

P/Y = 4  and C/Y = 4

N = 5.5

FV = 3000

I/Y = 4.5

CPT PV ==> -2820

What ?!?!!

How can this happen?

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3000/(1+0.045/4)22 = 2,345.489 yes

3000/(1+0.045/4)5.5 = 2,820.98 no

Under P1, your calculator will automatically set C/Y=1.  So you end up with 22 compounding periods at 1.125% per period.  Under P2, N has to be 22, not 5.5.

“Mmmmmm, something…” - H. Simpson

breadmaker wrote:

3000/(1+0.045/4)22 = 2,345.489 yes

3000/(1+0.045/4)5.5 = 2,820.98 no

Under P1, your calculator will automatically set C/Y=1.  So you end up with 22 compounding periods at 1.125% per period.  Under P2, N has to be 22, not 5.5.

Thank you so much.