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

[WeaponMaster]

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?

[breadmaker]

3000/(1+0.045/4)²² = 2,345.489

3000/(1+0.045/4)^5.5 = 2,820.98

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.

[WeaponMaster]

@breadmaker

3000/(1+0.045/4)²² = 2,345.489

3000/(1+0.045/4)^5.5 = 2,820.98

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.

[mann111]

For second try you need to use the annualised rate. 1.125 annualised to 4.5765 and use N =5.5.

[breadmaker]

@mann111

For second try you need to use the annualised rate. 1.125 annualised to 4.5765 and use N =5.5.

Compounding at 4.5765% annually is algebraically equivalent to compounding at 4.5% quarterly.