Let \(r_{m}\) be the interest rate with \(m\) compoundings per year, for example, \(m=12\) means monthly compounding.

(a) Derive the formula to convert \(r_{m}\) to \(r_{n}\) for general \(m, n=1,2,4,12\).

(b) Let \(r_{c}\) be the continuous compounding rate. Derive the formula to convert \(r_{m}\) to \(r_{c}\) and vice versa.

(c) Convert a simple add-on rate, \(r_{0}\), to a compounded rate \(r_{m}(m=\) \(1,2,4,12\) ), and vice versa.

(d) Convert a simple add-on rate, \(r_{0}\), to a continuously compounded rate, \(r_{c}\), and vice versa.

(e) For \(m

(f) Convert a simple (add-on) Act/360 rate, \(r_{1}\) to a simple (add-on) Act/365 rate, \(r_{2}\).

Hint: Compute the 1-year future value of unit currency invested at each rate and use the law of one price.