Ella has just retired and has received a lump sum pay-out of $1,800,000. She invests part of this pay-out in a perpetual investment which earns 4% per annum and provides a perpetual income to her of $30,000 per year (assuming end-of-year withdrawals). She puts the rest of the pay out in another investment in the form of a growing perpetuity (growth rate of 2% pa) which earns 4% pa. She wants to make annual withdrawals (starting in one year) from this growing perpetuity to fund some holidays.

Required

(i) Calculate how much Ella has invested in the perpetual investment.

(ii) Show how much extra Ella can expect to spend each year (assuming end-of-year withdrawals), over and above the $30,000 from the perpetual investment, from the growing perpetuity. Note: ignore tax in your calculations.