Question

Bank A pays 8% interest, compounded quarterly, on its money market account. The managers of bank B want its money market account’s effective annual rate to equal that of Bank A, but Bank B will compound interest on a monthly basis. What nominal, or quoted, rate must bank B set?

Answer 1

EAR=[(1+APR/m)^m]-1
where m=compounding periods

EAR for Bank A=[(1+0.08/4)^4]-1

=0.08243216

For Bank B:

0.08243216=[(1+APR/12)^12]-1

(1+0.08243216)=(1+APR/12)^12

APR=[(1+0.08243216)^(1/12)-1]*12

=7.95%(Approx).