On September $30,2023,$ Cullumber Inc. issued $$3,340,000$ of $10-$year, $8\%$ convertible bonds for $$3,841,000.$ The bonds pay interest on March $31$ and September $30$ and mature on September $30,2033.$ Each $$1,000$ bond can be converted into $80$ no par value common shares. In addition, each bond included $20$ detachable warrants. Each warrant can be used to purchase one common share at an exercise price of $$15.$ Immediately after the bond issuance, the warrants traded at $$3$ each. Without the warrants and the conversion rights, the bonds would have been expected to sell for $$3,507,000.$

On March $23,2026,$ half of the warrants were exercised. The common shares of Cullumber were trading at $$20$ each on this day.

Immediately after the payment of interest on the bonds, on September $30,2028,$ all bonds outstanding were converted into common shares. Assume the entity follows IFRS.

$($a$)$ Calculate the effective rate $($yield rate$)$ for the bonds