Invito, invitará

Invito, invitará
 

Antosch-and-Lin.com "Sentence of the Day" had:
Si me ayudas a limpiar, te invito a cenar.
If you help me clean up I will invite you out for dinner.

Would this be better?
Si me ayudas a limpiar, te invitaré a cenar.

How would it actually be said?

The future tense is used less in Spanish than in English. I seems cumbersome to change tense in the same sentences anyway,. In the sentence that Antosch and Lin provided the future is implied, and therefore the future tense in not necessary.

Many times I hear Spanish speakers using the present tense in English when a native speaker would use the future tense.

The Spanish present tense form of 'invitar' may be translated into any one of the following English forms (assume a first person):
I do invite
I invite
I am inviting
I will invite (near future)