Noah wants to put $1,000 in a savings account with a 1.5% annual interest rate. how much more money will he have after one year if it is compounded monthly versus no compounding?

Assuming that the 1.5% annual interest is split into monthly basis with the same amount, then the monthly interest should be: 1.5%/12= 0.125%.
If you put $1000 for annual interest, the saving account would become: $1000*(100%+1.5%)= $1015

If you put $1000 for monthly interest, the saving account would become: ($1000*(100%+0.125%)= $1000*1.0151035559= $1015.10

Then, the money difference should be:  $1015.10-$1015= $0.10