On 1 Jan 2007, Peter celebrates his 30 year old birthday. As a birth commitment, Peter joins a 15 year-contribution Annuity Plan. The annual contribution will be fixed at $28,800 for 15 years. The first annual premium is payable on 31 Dec 2007. Peter chooses to retire at age 60.The Annuity Plan pays a fixed amount every year forever after he retires. The payment from the Annuity Plan will be made at the end of each year. Assuming the long term interest rate is 4.84% per annum. All calculation is based on this rate.
a) What is the sum of gross amount of money that Peter contributes?
b) What will be the future value of the annuity when Peter becomes 45 years old (i.e. the day
after he will have paid the last premium)?
c) What will be the future value of the annuity when Peter celebrates his 60 year old birthday?
d) How much Peter could receive every year from the Annuity Plan after he retires?
Elain, Ming, Wong: We don't do homework for you. If you show thinking or work, we will generally critique it.
To answer these questions, we need to calculate the present value, future value, and annuity payments using the given information and the formula for compound interest. Let's go step by step:
a) The sum of the gross amount of money Peter contributes is obtained by multiplying the annual contribution by the number of years. In this case, Peter contributes $28,800 for 15 years:
Gross amount of money contributed = Annual contribution * Number of years
= $28,800 * 15
= $432,000
Therefore, the sum of the gross amount of money that Peter contributes is $432,000.
b) To find the future value of the annuity when Peter becomes 45 years old, we need to calculate the compound interest on an annuity. The formula for the future value of an annuity is:
Future Value = Annual payment * [((1 + interest rate)^number of years) - 1] / interest rate
In this case, the future value will be calculated for 15 years from the age of 30 to 45, with an annual payment of $28,800 and an interest rate of 4.84% per annum. Plugging these values into the formula:
Future Value = $28,800 * [((1 + 0.0484)^15) - 1] / 0.0484
Using a calculator or spreadsheet, the future value of the annuity when Peter becomes 45 years old is approximately $567,445.
c) Similarly, to find the future value of the annuity when Peter celebrates his 60th birthday, we again use the future value formula. Now, the future value will be calculated for 30 years from the age of 30 to 60, with an annual payment of $28,800 and an interest rate of 4.84% per annum. Plugging these values into the formula:
Future Value = $28,800 * [((1 + 0.0484)^30) - 1] / 0.0484
Using a calculator or spreadsheet, the future value of the annuity when Peter celebrates his 60th birthday is approximately $1,546,597.
d) Lastly, to calculate how much Peter could receive every year from the Annuity Plan after he retires, we use the concept of a perpetuity. A perpetuity is an infinite series of equal payments received at regular intervals. The formula for the present value of a perpetuity is:
Present Value = Annual payment / Interest rate
In this case, Peter will receive annual payments after he retires. The annual payment amount can be calculated using the present value formula, where the present value is the future value of the annuity we calculated in part c. Plugging these values into the formula:
Annual payment = Future Value / Interest rate
Annual payment = $1,546,597 / 0.0484
Using a calculator or spreadsheet, the amount Peter could receive every year from the Annuity Plan after he retires is approximately $31,944.17 (rounded to the nearest cent).
Please note that these calculations are based on the given interest rate and assumptions. It's always a good idea to consult a financial advisor or professional for personalized advice.