Question 3 (10 marks)

Your uncle Khaled is celebrating his 33^th birthday today and wants to start saving for his retirement at the age of 63. He wants to be able to withdraw AED 100,000 from his saving account on each birthday for 20 years following his retirement. The first withdraw will be on his 64^th birthday. Your uncle intends to invest his money in a local bank in Abu Dhabi that offers 7% interest rate per year. He wants to make equal payments on each birthday into the account established in the local bank for his retirement fund.

1. If your uncle starts making these deposits on his 33^th birthday and continues to make deposits until he is 63, what amount must he deposit annually to be able to make the desired withdrawals at retirement? (4 marks)
2. If your uncle has just inherited a large sum of money, so instead of making equal payments, he has decided to pay one lump sum payment on his 33^th birthday to cover his retirement needs. What amount does he have to deposit? (2 marks)
3. If your uncles employer informs your uncle that he will contribute AED 1,000 to your uncle account every year. Also, if your uncle expects AED100,000 from another investment on his 53^th birthday, which he will also put into the retirement account. What amount must he deposit annually now to be able to make the desired withdrawals at retirement. (4 marks)