Discount rate, convertible debt and the effect of time

The way I understand it is that there are three main parameters to a convertible debt investment.

1. An investment amount
2. A discount rate
3. A trigger event

Now under most of the examples I have seen, a trigger event for a given investment will occur, a post money valuation will be made based of the subsequent investment, at that point the convertible debt will be converted and a discount rate applied to it to calculate the initial investors final equity amount.

However I have on numerous occasions seen the discount rate being referred to as an "interest rate" and I stand confused in trying to understand if the length of time till the trigger event somehow effects the final discount rate of a convertible debt investment.

So say for example you negotiate a convertible debt investment with a 12% discount rate, does this mean that if the trigger event occurs in 1 month you might only have a 1% discount rate?

Fundamentally what I am asking is, does time have an effect on the discount rate or is this a set value regardless of the period of time elapsed till the trigger event? If the value is set, why is it often referred to as an interest rate?

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The definition of "discount" is what the convertible debt holder would be rewarded as an early investor. If the Priced round comes in @ $\$1.00$per share and the convertible debt holder has a 25% discount then they would convert their loan at$\$1.00 \times (1-0.25)$ or $\$0.75\$ per share.