Question

If the APR is 7% with monthly compounding, compute the quarterly rate

Answer 1

let the quarterly rate be i

then (1+i)^4 = (1+.07/12)^12
take 4th root of both sides

1+i = 1.0058333..^4
1+i = 1.023538
i = .023538 or 2.3538% per quarter

times 4, gives us
9.4153% per annum compounded quarterly.

Answer 2

Monthly rate=0.07/12=0.005833

Quarterly rate=(1+Monthly rate)^3-1
=(1+0.005833)^3-1
=1.017601-1
=0.017601
=1.76%