$($c$)$ Define $d^{(\frac{1}{m})}$ to be the nominal discount rate payable once every $m$ years. This means that the borrower pays discount at an effective rate of

$\frac{d^{(\frac{1}{m})}}{\frac{1}{m}}=m{d}^{(\frac{1}{m})}$

per $m$ year period.

Find a formula that gives $d^{(\frac{1}{m})}$ in terms of $i^{(\frac{1}{m})}.$

$d^{(\frac{1}{m})}=$

Find a formula that gives $d^{(\frac{1}{m})}$ in terms of $d.$

$d^{(\frac{1}{m})}=$