Question

The parent of a newborn child invest $500 in a plan

Answer 1

The child will have $2895.81 when it turns 18.

Explanation:

Semiannual compounding corresponds to compounding 5% twice a year.

After 1st (6mo) period, the initial deposit $500 grows to 500*1.05. After the second period, it grows to 500*1.05*1.05. After the n-th period, it grows to
`500\cdot 1.05^n`.

To answer the question we need to consider the fact that 18 years correspond to 36 half-year periods, and then we're ready to roll:

`X = 500\cdot 1.05^(36)=2895.81`

The child will have $2895.81 when it turns 18.