Step 1: Identify the time expression.
The phrase “by the time you reach your home” refers to a
specific point in the future.
Step 2: Recall the appropriate tense.
When an action will be completed before a certain future time,
we use the future perfect tense:
\[
\text{will have + past participle}
\]
Step 3: Analyse the options.
Will have reached — future perfect; correctly shows completion before a future time.
Is reaching — present continuous; incorrect for future completion.
Would have reached — conditional perfect; used for unreal past situations.
Will reach — simple future; does not emphasize completion before a future point.
Step 4: Select the correct option.
Hence, the correct answer is
\[
\boxed{\text{Will have reached}}
\]