Federal Court Justice Bernard Judy will turn 61 on the 30th June 2023. It is expected that on that day he will also receive payment of $250,000 from his mother's estate. His Honour plans to retire at the compulsory age of 70 and has an investment horizon of 15 years beyond that until he is 85 years old. The judge believes that, commencing in July this year, he will be able to save and invest $7,500 each month until the time when he retires. He will make the first of these monthly deposits on his 61st birthday.

Upon retirement the Judge wishes to receive a monthly pension of $20,000 to support him in the lifestyle to which he is accustomed. The pension is expected to continue from his retirement until the Judge's 85th birthday at which point he plans to have $1 million dollars remaining as a balance in his retirement funds. He expects to receive his first monthly pension payment 1 month after his retirement.

Justice Judy understands that his monthly savings and the $250,000 inheritance will not be enough to fund everything he hopes to achieve with his retirement fund and he plans to contribute a lump sum to start the fund. To establish the retirement fund Justice Judy intends to sell down financial assets currently held by him in blind trust in order to fund the planned annuity. His Honour intends to invest aggressively until his retirement at 70 during which time he expects investment earnings of 9% per annum (compounded monthly). Following retirement his investment will be more conservative and he hopes to achieve a return of 5% per annum (compounded monthly).

(i)     The judge has asked you to calculate the amount he needs to invest as at the 30th June to ensure that his retirement account will hold sufficient funds when he turns 70 and retires.

(ii)     Please also calculate the value of funds under management at the point of retirement (when the judge turns 70 years old).