Bank Identification Number Check Digit Formula Question

Alright, so I am suppose to use the bank indentification number check digit formula to see if it can detect a check with tranposed digits.

The correct bank ident number is 314970664

The incorrect bank indent # is 319470664

The "4" at the end of the number is the check digit.

Bank Ident. Number Check Digit Formula:

a0 ≡ (7a + 3a + 9a + 7a + 3a + 9a + 7a +3a) mod 10

a0 ≡ (7*3 + 3*1 + 9*9 + 7*4 + 3*7 + 9*0 + 7*6 + 3*6 )

≡ 21 + 3 + 81 + 28 + 21 + 0 + 42 + 18

≡ 1 + 3 + 1 + 8 + 1 + 0 + 2 + 8*; The **sum = 24 For some reason* my book drops the first digit and keeps the second digit or ones digit, I have no clue why it does this.

≡ 24 ≡ 4 (mod 10)

The difference between 24 and 4 is 20, which is a multiple of 10.

Therefore the check digit did not catch the error.

Does there seem to be any problems with my solution?

cheers.