債券の利率の数式

最近リスク管理を勉強しながら債券の利回りを計算しています。特に利札付きの物が分かりにくい。
The cash flows for coupon-paying bonds are fairly simple. Beginning from the first year, coupon payments of the amount C are made at year-end, where C=P*(CR), CR being the coupon rate and P being par value. In the final year (at expiry), C+P is made. Discounting back at the yield rate y, we get:
price = C/(1+y) + C/(1+y)^2 + C/(1+y)^3 + ... + C/(1+y)^(N-1) + (C+P)/(1+y)^N
for a bond with a lifetime of N years.
From this formula, one can multiply both sides by (1+y)^N, obtaining:
price*(1+y)^N = C(1+y)^(N-1) + C(1+y)^(N-2) + ... + C(1+y) + C
This can be simplified using a formula for geometric series, where r = 1+y, i.e. 1 + r + r^2 + ...+ r^(N-1) = (r^N-1)/(r-1)
so:
price*(1+y)^N = C((1+y)^N-1)/y
I am not sure that this can be solved analytically for y, given C, price, and N are known.
However, I recently saw a formula for the yield rate in the form of:
y = (CR + (par-price)/N)/(.4*par + .6*price)
The derivation of this formula is a mystery to me. 謎の導出。