Your parents wish to save $30,000 for your wedding scheduled on 31 December 2023. They will start the first monthly deposit by the end of this month, 30 June 2022, and earn J12 = 4% p.a.

1) What is the regular deposit required per month?

2) Suppose that after three deposits, the interest rate rises to J12 = 4.5% p.a. Determine the new deposit size required to meet the original $30,000 goal

3) If they are ready to save $5,000 per month, how fast can they reach $30,000 under the new interest rate?

4) How would your answer to Q1 change if the interest was compounded fortnightly? weekly? daily? Provide an explanation with a sanity check