Is the parenthesis in the sentence ok?

[wang.cupid]

Hello, to be exact is used in the following sentence as a parenthesis(I guess this is a correct expression for it). Does it look natural? By the way, are there other any grammatical errors.

I cannot find my diploma because I graduated from the senior high school a long time ago, to be exact, 13 years ago, and I accidentally lost it.

[minnieuk]

It should be:

I cannot find my diploma because I graduated from the senior high school a long time ago, 13 years ago to be exact, and I have lost it.

Also, you don't need to say accidentally because it is already implied in lost. Nobody thinks you lost it on purpose.