(d) You are working and just turned 30 years old. You will retire when you turn 55 years old. You are now planning for retirement. Currently you spend $2,000 per month. You hope to improve your lifestyle. You anticipate an increase in expenses of $50 per month every year for the first 25 years. This means that your monthly expenses will be $2,050 per month one year from now, $2,100 per month two years from now, and so on. The increase in expenses is non-inflationary, as it could be due to your personal preference of eating out more often at fancier restaurants, taking up a gym membership, and so on. The increase in expenses will stop upon retirement. To achieve this goal, you will be investing in a fund earning 5% effective rate per year, with level monthly payments A made to the fund, starting from now for 25 years. The 1st monthly withdrawal will be made upon retirement at the age of 55. The payments to the fund and withdrawals are to be done at the beginning of each month. Assume that the inflation rate is is 0% before retirement, and is 2% effective per year throughout the retirement period. Assume you are planning to use these funds to survive until age 100. Note that this also means that you will not have anymore funds left in your account when you turn 100 years old. Determine the minimum value of A such that you have sufficient funds to survive until age 100. In your calculations, include a time diagram to illustrate your working. [14] (d) You are working and just turned 30 years old. You will retire when you turn 55 years old. You are now planning for retirement. Currently you spend $2,000 per month. You hope to improve your lifestyle. You anticipate an increase in expenses of $50 per month every year for the first 25 years. This means that your monthly expenses will be $2,050 per month one year from now, $2,100 per month two years from now, and so on. The increase in expenses is non-inflationary, as it could be due to your personal preference of eating out more often at fancier restaurants, taking up a gym membership, and so on. The increase in expenses will stop upon retirement. To achieve this goal, you will be investing in a fund earning 5% effective rate per year, with level monthly payments A made to the fund, starting from now for 25 years. The 1st monthly withdrawal will be made upon retirement at the age of 55. The payments to the fund and withdrawals are to be done at the beginning of each month. Assume that the inflation rate is is 0% before retirement, and is 2% effective per year throughout the retirement period. Assume you are planning to use these funds to survive until age 100. Note that this also means that you will not have anymore funds left in your account when you turn 100 years old. Determine the minimum value of A such that you have sufficient funds to survive until age 100. In your calculations, include a time diagram to illustrate your working. [14]
