If payments start NOW (as is specified in problem), then the PV

is calculated using immediate payment formula:

this results in 643.67

If he waits 2 months, then the PV in 2 months will be 637.30;

this needs to be discounted for a further 2 months:

637.30 / 1.01^2 = 624.74

So difference is 643.67 - 624.74 = 18.93

The given answer of 12.68 is not correct: it does not assume

an immediate payment.

It would be correct if 1st payment was not immediate, but in 1 month.